chap1-rev-problems.xml

<?xml version="1.0"?>


<!-- This file was originally part of the book     -->
<!--   Modeling, Functions, and Graphs   -->
<!--           4th                                     -->
<!-- Copyright (C) Katherine Yoshiwara      -->

<exercises xml:id="chap1-rev-problems"  xmlns:xi="http://www.w3.org/2001/XInclude">
    <title>Review Problems</title>

<exercisegroup >
        <introduction><p>Write and graph a linear equation for each situation. Then answer the questions.</p></introduction>

    <exercise number="1">
        <statement><p>
            Last year, Pinwheel Industries introduced a new model calculator. It cost <m>\$2000</m> to develop the calculator and <m>\$20</m> to manufacture each one.
            <ol label="a">
                <li><p>Complete the table of values showing the total cost, <m>C</m>, of producing <m>n</m> calculators.</p><p>
                <sidebyside><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>n</m></cell>
                        <cell><m>100</m></cell>
                        <cell><m>500</m></cell>
                        <cell><m>800</m></cell>
                        <cell><m>1200</m></cell>
                        <cell><m>1500</m></cell>
                    </row>
                    <row>
                        <cell><m>C</m></cell>
                        <cell><m>\hphantom{0000}</m></cell>
                        <cell><m>\hphantom{0000}</m></cell>
                        <cell><m>\hphantom{0000}</m></cell>
                        <cell><m>\hphantom{0000}</m></cell>
                        <cell><m>\hphantom{0000}</m></cell>
                    </row>
                </tabular></sidebyside>
            </p></li>
            <li><p>Write an equation that expresses <m>C</m> in terms of <m>n</m>.</p></li>
            <li><p>Graph the equation by hand.</p></li>
            <li><p>What is the cost of producing <m>1000</m> calculators? Illustrate this as a point on your graph.</p></li>
            <li><p>How many calculators can be produced for <m>\$10,000</m>? Illustrate this as a point on your graph.</p></li>
            </ol>
        </p></statement>
        <answer><p>
            <ol label="a">
                <li><p><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>n</m></cell>
                        <cell><m>100</m></cell>
                        <cell><m>500</m></cell>
                        <cell><m>800</m></cell>
                        <cell><m>1200</m></cell>
                        <cell><m>1500</m></cell>
                    </row>
                    <row>
                        <cell><m>C</m></cell>
                        <cell><m>4000</m></cell>
                        <cell><m>12,000</m></cell>
                        <cell><m>18,000</m></cell>
                        <cell><m>26,000</m></cell>
                        <cell><m>32,000</m></cell>
                    </row>
                </tabular></p></li>
                <li><p><m>C = 20n + 2000</m></p></li>
                <li><p><image source="images/fig-ans-chap1-rev-1"  width="60%"><description>cost vs number</description></image> </p></li>
                <li><p><m>\$22,000</m></p></li>
                <li><p><m>400</m></p></li>
            </ol>
        </p></answer>
    </exercise>

    <exercise number="2">
        <statement><p>
            Megan weighed <m>5</m> pounds at birth and gained <m>18</m> ounces per month during her first year.
            <ol label="a">
                <li><p>Complete the table of values for Megan's weight, <m>w</m>, in terms of her age, <m>m</m>, in months.</p><p>
                <sidebyside><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>m</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>4</m></cell>
                        <cell><m>6</m></cell>
                        <cell><m>9</m></cell>
                        <cell><m>12</m></cell>
                    </row>
                    <row>
                        <cell><m>w</m></cell>
                        <cell><m>\hphantom{0000}</m></cell>
                        <cell><m>\hphantom{0000}</m></cell>
                        <cell><m>\hphantom{0000}</m></cell>
                        <cell><m>\hphantom{0000}</m></cell>
                        <cell><m>\hphantom{0000}</m></cell>
                    </row>
                </tabular></sidebyside>
            </p></li>
            <li><p>Write an equation that expresses <m>2</m> in terms of <m>m</m>.</p></li>
            <li><p>Graph the equation by hand.</p></li>
            <li><p>How much did Megan weigh at <m>9</m> months? Illustrate this as a point on your graph.</p></li>
            <li><p>When did Megan weigh <m>9</m> pounds? Illustrate this as a point on your graph.</p></li>
            </ol>
        </p></statement>
    </exercise>

    <exercise number="3">
        <statement><p>The total amount of oil remaining in 2005 is estimated at <m>2.1</m> trillion barrels, and total annual consumption is about <m>28</m> billion barrels.
            <ol label="a">
                <li><p>Assuming that oil consumption continues at the same level, write an equation for the remaining oil, <m>R</m>, as a function of time, <m>t</m> (in years since 2005).</p></li>
                <li><p>Find the intercepts and graph the equation by hand.</p></li>
                <li><p>What is the significance of the intercepts to the world's oil supply?</p></li>
            </ol>
            </p></statement>
        <answer><p>
            <ol label="a">
                <li><p><m>R = 2100 - 28t</m></p></li>
                <li><p><m>(75, 0)</m>, <m>(0, 2100)</m></p></li>
                <li><p><m>t</m>-intercept: The oil reserves will be gone in 2080; <m>R</m>-intercept: There were <m>2100</m> billion barrels of oil reserves in 2005.</p></li>
            </ol>
        </p></answer>
    </exercise>

    <exercise number="4">
        <statement><p>The world's copper reserves were <m>950</m> million tons in 2004; total annual consumption was <m>16.8</m> million tons.
            <ol label="a">
                <li><p>Assuming that copper consumption continues at the same level, write an equation for the remaining copper reserves, <m>R</m>, as a function of time, <m>t</m> (in years since 2004).</p></li>
                <li><p>Find the intercepts and graph the equation by hand.</p></li>
                <li><p>What is the significance of the intercepts to the world's copper supply?</p></li>
            </ol>
            </p></statement>
    </exercise>

    <exercise number="5">
        <statement><p>The owner of a movie theater needs to bring in <m>\$1000</m> at each screening in order to stay in business. He sells adult tickets at <m>\$5</m> apiece and children's tickets at <m>\$2</m> each.
            <ol label="a">
                <li><p>Write an equation that relates the number of adult tickets, <m>A</m>, he must sell and the number of children's tickets, <m>C</m>.</p></li>
                <li><p>Find the intercepts and graph the equation by hand.</p></li>
                <li><p>If the owner sells <m>120</m> adult tickets, how many children's tickets must he sell?</p></li>
                <li><p>What is the significance of the intercepts to the sale of tickets?</p></li>
            </ol>
            </p></statement>
        <answer><p>
            <ol label="a">
                <li><p><m>2C + 5A = 1000</m></p></li>
                <li><p><m>(500, 0)</m>, <m>(0, 200)</m>
                <image source="images/fig-ans-chap1-rev-5"  width="45%">
                  <description>
                    Adult tickets vs Children's tickets
                  </description>
                </image>
            </p></li>
                <li><p><m>C</m>-intercept: If no adult tickets are sold, he must sell <m>500</m> children's tickets; <m>A</m>-intercept: If no children's tickets are sold, he must sell <m>200</m> adult tickets.</p></li>
            </ol>
        </p></answer>
    </exercise>

    <exercise number="6">
        <statement><p>Alida plans to spend part of her vacation in Atlantic City and part in Saint-Tropez. She estimates that after airfare her vacation will cost <m>\$60</m> per day in Atlantic City and <m>$100</m> per day in Saint-Tropez. She has <m>\$1200</m> to spend after airfare.
            <ol label="a">
                <li><p>Write an equation that relates the number of days, <m>C</m>, Alida can spend in Atlantic City and the number of days, <m>T</m>, in Saint-Tropez.</p></li>
                <li><p>Find the intercepts and graph the equation by hand.</p></li>
                <li><p>If Alida spends <m>10</m> days in Atlantic City, how long can she spend in Saint-Tropez?</p></li>
                <li><p>What is the significance of the intercepts to Alida's vacation?</p></li>
            </ol>
            </p></statement>
    </exercise>

</exercisegroup>
<exercisegroup cols="3"><introduction><p>Graph each equation on graph paper. Use the most convenient method for each problem.</p></introduction>

    <exercise number="7">
        <statement>
            <p><m>4x - 3y = 12</m></p>
        </statement>
        <answer><p><image source="images/fig-ans-chap1-rev-7"  width="40%"><description>line in fourth quadrant</description></image>
        </p></answer>
     </exercise>

    <exercise number="8">
        <statement>
            <p><m>\dfrac{x}{6}- \dfrac{y}{12}= 1</m></p>
        </statement>
    </exercise>

    <exercise number="9">
        <statement>
            <p><m>50x = 40y - 20,000</m></p>
        </statement>
        <answer><p><image source="images/fig-ans-chap1-rev-9"  width="40%"><description>line in second quadrant</description></image>
        </p></answer>
    </exercise>

    <exercise number="10">
        <statement>
            <p><m>1.4x + 2.1y = 8.4</m></p>
        </statement>
    </exercise>

    <exercise number="11">
        <statement>
            <p><m>3x - 4y = 0</m></p>
        </statement>
        <answer><p><image source="images/fig-ans-chap1-rev-11"  width="40%"><description>line through origin</description></image>
        </p></answer>
     </exercise>

    <exercise number="12">
        <statement>
            <p><m>x = -4y</m></p>
        </statement>
    </exercise>

    <exercise number="13">
        <statement>
            <p><m>4x = -12</m></p>
        </statement>
        <answer><p><image source="images/fig-ans-chap1-rev-13"  width="40%"><description>vertical line</description></image>
        </p></answer>
    </exercise>

    <exercise number="14">
        <statement>
            <p><m>2y - x = 0</m></p>
        </statement>
    </exercise>
    
</exercisegroup>
<exercisegroup cols="2"><introduction><p>Which of the following tables describe functions? Explain.</p></introduction>
    <exercise number="15">
        <statement>
            <p><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>-2</m></cell>
                        <cell><m>-1</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>1</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>3</m></cell>
                    </row>
                    <row>
                        <cell><m>y</m></cell>
                        <cell><m>6</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>1</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>6</m></cell>
                        <cell><m>8</m></cell>
                    </row>
                </tabular></p>
        </statement>
        <answer><p>A function: Each <m>x</m> has exactly one associated <m>y</m>-value.</p></answer>
    </exercise>

    <exercise number="16">
        <statement>
            <p><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>p</m></cell>
                        <cell><m>3</m></cell>
                        <cell><m>-3</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>-2</m></cell>
                        <cell><m>-2</m></cell>
                        <cell><m>0</m></cell>
                    </row>
                    <row>
                        <cell><m>q</m></cell>
                        <cell><m>2</m></cell>
                        <cell><m>-1</m></cell>
                        <cell><m>4</m></cell>
                        <cell><m>-4</m></cell>
                        <cell><m>3</m></cell>
                        <cell><m>0</m></cell>
                    </row>
                </tabular></p>
        </statement>
    </exercise>

    <exercise number="17">
        <statement>
            <p><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell>Student</cell>
                        <cell><line>Score on</line><line>IQ test</line></cell>
                        <cell><line>Score on</line><line>SAT test</line></cell>
                    </row>
                    <row>
                        <cell>(A)</cell>
                        <cell><m>118</m></cell>
                        <cell><m>649</m></cell>
                    </row>
                    <row>
                        <cell>(B)</cell>
                        <cell><m>98</m></cell>
                        <cell><m>450</m></cell>
                    </row>
                    <row>
                        <cell>(C)</cell>
                        <cell><m>110</m></cell>
                        <cell><m>590</m></cell>
                    </row>
                    <row>
                        <cell>(D)</cell>
                        <cell><m>105</m></cell>
                        <cell><m>520</m></cell>
                    </row>
                    <row>
                        <cell>(E)</cell>
                        <cell><m>98</m></cell>
                        <cell><m>490</m></cell>
                    </row>
                    <row>
                        <cell>(F)</cell>
                        <cell><m>122</m></cell>
                        <cell><m>680</m></cell>
                    </row>
                </tabular></p>
        </statement>
        <answer><p>Not a function: The IQ of <m>98</m> has two possible SAT scores.</p></answer>
    </exercise>

    <exercise number="18">
        <statement>
            <p><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell>Student</cell>
                        <cell><line>Correct answers</line><line>on math quiz</line></cell>
                        <cell><line>Quiz</line><line>grade</line></cell>
                    </row>
                    <row>
                        <cell>(A)</cell>
                        <cell><m>13</m></cell>
                        <cell><m>85</m></cell>
                    </row>
                    <row>
                        <cell>(B)</cell>
                        <cell><m>15</m></cell>
                        <cell><m>89</m></cell>
                    </row>
                    <row>
                        <cell>(C)</cell>
                        <cell><m>10</m></cell>
                        <cell><m>79</m></cell>
                    </row>
                    <row>
                        <cell>(D)</cell>
                        <cell><m>12</m></cell>
                        <cell><m>82</m></cell>
                    </row>
                    <row>
                        <cell>(E)</cell>
                        <cell><m>16</m></cell>
                        <cell><m>91</m></cell>
                    </row>
                    <row>
                        <cell>(F)</cell>
                        <cell><m>18</m></cell>
                        <cell><m>95</m></cell>
                    </row>
                </tabular></p>
        </statement>
   </exercise>

</exercisegroup>


    <exercise number="19">
        <statement><p>The total number of barrels of oil pumped by the AQ oil company is given by the formula <m>N(t) = 2000 + 500t</m>, where <m>N</m> is the number of barrels of oil <m>t</m> days after a new well is opened. Evaluate <m>N(10)</m> and explain what it means.</p>
        </statement>
        <answer><p><m>N(10) = 7000</m>: Ten days after the new well is opened, the company has pumped a total of <m>7000</m> barrels of oil.</p></answer>
    </exercise>

    <exercise number="20">
        <statement><p>The number of hours required for a boat to travel upstream between two cities is given by the formula <m>H(v) = \dfrac{24}{v - 8}</m>, where <m>v</m> represents the boat's top speed in miles per hour. Evaluate <m>H(16)</m> and explain what it means.</p>
        </statement>
    </exercise>

<exercisegroup cols="4"><introduction><p>Which of the following graphs represent functions?</p></introduction>
    <exercise number="21">
        <statement><p><image source="images/fig-chap1-rev-21"  width="90%"><description>curve</description></image> </p>
        </statement>
        <answer><p>Function</p></answer>
    </exercise>

    <exercise number="22">
        <statement><p><image source="images/fig-chap1-rev-22"  width="90%"><description>curve</description></image> </p>
        </statement>
    </exercise>

    <exercise number="23">
        <statement><p><image source="images/fig-chap1-rev-23"  width="90%"><description>curve</description></image> </p>
        </statement>
        <answer><p>Not a function</p></answer>
    </exercise>

    <exercise number="24">
        <statement><p><image source="images/fig-chap1-rev-24"  width="90%"><description>curve</description></image> </p>
        </statement>
   </exercise>

</exercisegroup>

<exercisegroup ><introduction><p>Evaluate each function for the given values.</p></introduction>
    <exercise number="25">
        <statement><p><m>F(t)=\sqrt{1+4t^2}</m>, <m>~~F(0)~~</m> and <m>~~F(-3)</m> </p>
        </statement>
        <answer><p><m>F(0) = 1, ~~F(-3) =\sqrt{37}</m></p></answer>
    </exercise>

    <exercise number="26">
        <statement><p><m>G(x)=\sqrt[3]{x-8}</m>, <m>~~G(0)~~</m> and <m>~~G(20)</m>  </p>
        </statement>
    </exercise>

    <exercise number="27">
        <statement><p><m>h(v)=6-\abs{4-2v} </m>, <m>~~h(8)~~</m> and <m>~~h(-8)</m> </p>
        </statement>
        <answer><p><m>h(8) = -6, ~~h(-8) = -14</m></p></answer>
    </exercise>

    <exercise number="28">
        <statement><p><m>m(p)=\dfrac{120}{p+15} </m>, <m>~~m(5)~~</m> and <m>~~m(-40)</m> </p>
        </statement>
   </exercise>

</exercisegroup>
<exercisegroup><introduction><p>Refer to the graphs shown for Problems 29 and 30.</p></introduction>

    <exercise number="29">
        <statement><p><ol label="a">
            <li><p>Find <m>f (-2)</m> and <m>f (2)</m>.</p></li>
            <li><p>For what value(s) of <m>t</m> is <m>f (t) = 4</m>?</p></li>
            <li><p>Find the <m>t</m>- and <m>f(t)</m>-intercepts of the graph.</p></li>
            <li><p>What is the maximum value of <m>f</m>? For what value(s) of <m>t</m> does <m>f</m> take on its maximum value?</p></li>
        </ol>
        <image source="images/fig-chap1-rev-29"  width="35%">
          <description>
            curve
          </description>
        </image>
        </p>
        </statement>
        <answer><p><ol label="a">
            <li><p><m>f (-2) = 3, ~~f (2) = 5</m></p></li>
            <li><p><m>t = 1, ~~t = 3</m></p></li>
            <li><p><m>t</m>-intercepts <m>(-3, 0), (4, 0)</m>; <m>f (t)</m>-intercept: <m>(0, 2)</m></p></li>
            <li><p>Maximum value of <m>5</m> occurs at <m>t = 2</m></p></li>
        </ol>
        </p></answer>
    </exercise>

    <exercise number="30">
        <statement><p><ol label="a">
            <li><p>Find <m>P(-3)</m> and <m>P(3)</m>.</p></li>
            <li><p>For what value(s) of <m>z</m> is <m>P(z) = 2</m>?</p></li>
            <li><p>Find the <m>z</m>- and <m>P(z)</m>-intercepts of the graph.</p></li>
            <li><p>What is the minimum value of <m>P</m>? For what value(s) of <m>z</m> does <m>P</m> take on its minimum value?</p></li>
        </ol>
        <image source="images/fig-chap1-rev-30"  width="35%">
          <description>
            curve
          </description>
        </image>
        </p>
        </statement>
   </exercise>

</exercisegroup>

<exercisegroup ><introduction><p>Graph the given function on a graphing calculator. Then use the graph to solve the equations and inequalities. Round your answers to one decimal place if necessary.</p></introduction>

    <exercise number="31">
        <statement><p><m>y=\sqrt[3]{x} </m>
        <ol label="a" cols="2">
            <li><p>Solve <m>\sqrt[3]{x} = 0.8</m></p></li>
            <li><p>Solve <m>\sqrt[3]{x} = 1.5</m></p></li>
            <li><p>Solve <m>\sqrt[3]{x}\gt 1.7 </m></p></li>
            <li><p>Solve <m>\sqrt[3]{x}\le 1.26 </m></p></li>
        </ol>
        </p>
        </statement>
        <answer><p><ol label="a" cols="2">
            <li><p><m>x = \dfrac{1}{2}= 0.5</m></p></li>
            <li><p><m>x = \dfrac{27}{8}\approx 3.4</m></p></li>
            <li><p><m>x \gt 4.9</m> </p></li>
            <li><p><m>x\le 2.0</m></p></li>
        </ol>
        </p></answer>
    </exercise>

    <exercise number="32">
        <statement><p><m>y=\dfrac{1}{x} </m>
        <ol label="a" cols="2">
            <li><p>Solve <m>\dfrac{1}{x} = 2.5</m></p></li>
            <li><p>Solve <m>\dfrac{1}{x} = 1.3125</m></p></li>
            <li><p>Solve <m>\dfrac{1}{x}\ge 2.\overline{2} </m></p></li>
            <li><p>Solve <m>\dfrac{1}{x}\lt 5</m></p></li>
        </ol>
        </p>
        </statement>
    </exercise>

    <exercise number="33">
        <statement><p><m>y=\dfrac{1}{x^2} </m>
        <ol label="a" cols="2">
            <li><p>Solve <m>\dfrac{1}{x^2} = 0.03</m></p></li>
            <li><p>Solve <m>\dfrac{1}{x^2} = 6.25</m></p></li>
            <li><p>Solve <m>\dfrac{1}{x^2}\gt 0.16 </m></p></li>
            <li><p>Solve <m>\dfrac{1}{x^2}\le 4</m></p></li>
        </ol>
        </p>
        </statement>
        <answer><p><ol label="a" cols="2">
            <li><p><m>x\approx\pm 5.8 </m></p></li>
            <li><p><m>x = \pm 0.4</m></p></li>
            <li><p><m>-2.5\lt x \lt 0</m> or <m>0\lt x\lt 2.5</m></p></li>
            <li><p><m>x\le -0.5</m> or <m>x\ge 0.5</m></p></li>
        </ol>
        </p></answer>
    </exercise>

    <exercise number="34">
        <statement><p><m>y=\sqrt{x} </m>
        <ol label="a" cols="2">
            <li><p>Solve <m>\sqrt{x} = 0.707</m></p></li>
            <li><p>Solve <m>\sqrt{x} = 1.7</m></p></li>
            <li><p>Solve <m>\sqrt{x}\lt 1.5 </m></p></li>
            <li><p>Solve <m>\sqrt{x}\ge 1.3 </m></p></li>
        </ol>
        </p>
        </statement>
    </exercise>

</exercisegroup>

<exercisegroup ><introduction><p>Evaluate each function.</p></introduction>
    <exercise number="35">
        <statement><p><m>H(t)=t^2+2t</m>, <m>~~H(2a)~~</m> and <m>~~H(a+1)</m> </p>
        </statement>
        <answer><p><m>H(2a) =4a^2 + 4a, ~~H(a+1) =a^2+4a+3</m></p></answer>
    </exercise>

    <exercise number="36">
        <statement><p><m>F(x)=2-3x</m>, <m>~~F(2)+F(3)~~</m> and <m>~~F(2+3)</m>  </p>
        </statement>
    </exercise>

    <exercise number="37">
        <statement><p><m>f(x)=2x^2-4 </m>, <m>~~f(a)+f(b)~~</m> and <m>~~f(a+b)</m> </p>
        </statement>
        <answer><p><m>f (a) + f (b) = 2a^2 + 2b^2 - 8, ~~f (a + b) = 2a^2 + 4ab + 2b^2 - 4</m></p></answer>
    </exercise>

    <exercise number="38">
        <statement><p><m>G(t)=1-t^2 </m>, <m>~~G(3w)~~</m> and <m>~~G(s+1)</m> </p>
        </statement>
   </exercise>

</exercisegroup>

    <exercise number="39">
        <statement><p>A spiked volleyball travels <m>6</m> feet in <m>0.04</m> seconds. A pitched baseball travels <m>66</m> feet in <m>0.48</m> seconds. Which ball travels faster? </p>
        </statement>
        <answer><p>The volleyball</p></answer>
    </exercise>

    <exercise number="40">
        <statement><p>Kendra needs <m>412</m> gallons of Luke's Brand primer to cover <m>1710</m> square feet of wall. She uses <m>513</m> gallons of Slattery's Brand primer for <m>2040</m> square feet of wall. Which brand covered more wall per gallon? </p>
        </statement>
    </exercise>

    <exercise number="41">
        <statement><p>Which is steeper, Stone Canyon Drive, which rises <m>840</m> feet over a horizontal distance of <m>1500</m> feet, or Highway 33, which rises <m>1150</m> feet over a horizontal distance of <m>2000</m> feet? </p>
        </statement>
        <answer><p>Highway 33</p></answer>
    </exercise>

    <exercise number="42">
        <statement><p>The top of Romeo's ladder is on Juliet's window sill that is <m>11</m> feet above the ground, and the bottom of the ladder is <m>5</m> feet from the base of the wall. Is the incline of this ladder as steep as a firefighter's ladder that rises a height of <m>35</m> feet over a horizontal distance of <m>16</m> feet? </p>
        </statement>
    </exercise>

    <exercise number="43">
        <statement><p>The table shows the amount of oil, <m>B</m> (in thousands of barrels), left in a tanker <m>t</m> minutes after it hits an iceberg and springs a leak.</p><p>
        <sidebyside><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
            <row>
                <cell><m>t</m></cell>
                <cell><m>0</m></cell>
                <cell><m>10</m></cell>
                <cell><m>20</m></cell>
                <cell><m>30</m></cell>
            </row>
            <row>
                <cell><m>B</m></cell>
                <cell><m>800</m></cell>
                <cell><m>750</m></cell>
                <cell><m>700</m></cell>
                <cell><m>650</m></cell>
            </row>
        </tabular></sidebyside>
        <ol label="a">
            <li><p>Write a linear function for <m>B</m> in terms of <m>t</m>.</p></li>
            <li><p>Choose appropriate window settings on your calculator and graph your function.</p></li>
            <li><p>Give the slope of the graph, including units, and explain the meaning of the slope in terms of the oil leak.</p></li>
        </ol>
        </p>
        </statement>
        <answer><p>
        <ol label="a">
            <li><p><m>B = 800 - 5t</m></p></li>
            <li><p><image source="images/fig-ans-chap1-rev-43.jpg"  width="40%"><description>GC graph</description></image> </p></li>
            <li><p><m>m = -5</m> thousand barrels/minute: The amount of oil in the tanker is decreasing by <m>5000</m> barrels per minute.</p></li>
        </ol>
        </p></answer>
    </exercise>

    <exercise number="44">
        <statement><p>A traditional first experiment for chemistry students is to make <m>98</m> observations about a burning candle. Delbert records the height, <m>h</m>, of the candle in inches at various times <m>t</m> minutes after he lit it.</p><p>
        <sidebyside><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
            <row>
                <cell><m>t</m></cell>
                <cell><m>0</m></cell>
                <cell><m>10</m></cell>
                <cell><m>30</m></cell>
                <cell><m>45</m></cell>
            </row>
            <row>
                <cell><m>h</m></cell>
                <cell><m>12</m></cell>
                <cell><m>11.5</m></cell>
                <cell><m>10.5</m></cell>
                <cell><m>9.75</m></cell>
            </row>
        </tabular></sidebyside>
        <ol label="a">
            <li><p>Write a linear function for <m>h</m> in terms of <m>t</m>.</p></li>
            <li><p>Choose appropriate window settings on your calculator and graph your function.</p></li>
            <li><p>Give the slope of the graph, including units, and explain the meaning of the slope in terms of the candle.</p></li>
        </ol>
        </p>
        </statement>
    </exercise>

    <exercise number="45">
        <statement><p>An interior decorator bases her fee on the cost of a remodeling job. The accompanying table shows her fee, <m>F</m>, for jobs of various costs, <m>C</m>, both given in dollars.</p><p>
        <sidebyside><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
            <row>
                <cell><m>C</m></cell>
                <cell><m>5000</m></cell>
                <cell><m>10,000</m></cell>
                <cell><m>20,000</m></cell>
                <cell><m>50,000</m></cell>
            </row>
            <row>
                <cell><m>F</m></cell>
                <cell><m>1000</m></cell>
                <cell><m>1500</m></cell>
                <cell><m>2500</m></cell>
                <cell><m>5500</m></cell>
            </row>
        </tabular></sidebyside>
        <ol label="a">
            <li><p>Write a linear function for <m>F</m> in terms of <m>C</m>.</p></li>
            <li><p>Choose appropriate window settings on your calculator and graph your function.</p></li>
            <li><p>Give the slope of the graph, including units, and explain the meaning of the slope in terms of the the decorator's fee.</p></li>
        </ol>
        </p>
        </statement>
        <answer><p>
        <ol label="a">
            <li><p><m>F = 500 + 0.10C</m></p></li>
            <li><p><image source="images/fig-ans-chap1-rev-45.jpg"  width="40%"><description>GC graph</description></image> </p></li>
            <li><p><m>m = 0.10</m>: The fee increases by <m>\$0.10</m> for each dollar increase in the remodeling job.</p></li>
        </ol>
        </p></answer>
    </exercise>

    <exercise number="46">
        <statement><p>Auto registration fees in Connie's home state depend on the value of the automobile. The table below shows the registration fee, <m>R</m>, for a car whose value is <m>V</m>, both given in dollars.</p><p>
        <sidebyside><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
            <row>
                <cell><m>V</m></cell>
                <cell><m>5000</m></cell>
                <cell><m>10,000</m></cell>
                <cell><m>15,000</m></cell>
                <cell><m>20,000</m></cell>
            </row>
            <row>
                <cell><m>R</m></cell>
                <cell><m>135</m></cell>
                <cell><m>235</m></cell>
                <cell><m>335</m></cell>
                <cell><m>435</m></cell>
            </row>
        </tabular></sidebyside>
        <ol label="a">
            <li><p>Write a linear function for <m>R</m> in terms of <m>V</m>.</p></li>
            <li><p>Choose appropriate window settings on your calculator and graph your function.</p></li>
            <li><p>Give the slope of the graph, including units, and explain the meaning of the slope in terms of the registration fee.</p></li>
        </ol>
        </p>
        </statement>
    </exercise>

<exercisegroup cols="2"><introduction><p>Find the slope of the line segment joining each pair of points.</p></introduction>

    <exercise number="47">
        <statement><p><m>(-1, 4), ~(3, -2)</m> </p>
        </statement>
        <answer><p><m>\dfrac{-3}{2} </m></p></answer>
    </exercise>

    <exercise number="48">
        <statement><p><m>(5, 0), ~(2, -6)</m>  </p>
        </statement>
    </exercise>

    <exercise number="49">
        <statement><p><m>(6.2, 1.4), ~(-2.1, 4.8)</m> </p>
        </statement>
        <answer><p><m>\dfrac{-34}{83}\approx-0.4 </m></p></answer>
    </exercise>

    <exercise number="50">
        <statement><p><m>(0, -6.4), ~(-5.6, 3.2)</m>  </p>
        </statement>
    </exercise>

</exercisegroup>


    <exercise number="51"><statement><p>
        The planners at AquaWorld want the small water slide to have a slope of <m>25\%</m>. If the slide is <m>20</m> feet tall, how far should the end of the slide be from the base of the ladder?</p></statement>
        <answer><p><m>80</m> ft</p></answer>
    </exercise>

    <exercise number="52"><statement><p>
        In areas with heavy snowfall, the pitch (or slope) of the roof of an A-frame house should be at least <m>1.2</m>. If a small ski chalet is <m>40</m> feet wide at its base, how tall is the center of the roof?</p></statement>
    </exercise>

<exercisegroup cols="2"><introduction>
    <p>Find the coordinates of the indicated points, and then write an algebraic expression using function notation for the indicated quantities.</p></introduction>

    <exercise number="53"><statement><p>
        <ol label="a">
            <li><p><m>\Delta y</m> as <m>x</m> increases from <m>x_1</m> to <m>x_2</m></p></li>
            <li><p>The slope of the line segment joining <m>P</m> to <m>Q</m></p></li>
        </ol>
        <image source="images/fig-chap1-rev-53"  width="75%">
          <description>
            piecewise linear function f
          </description>
        </image>
    </p></statement>
    <answer><p>
        <ol label="a">
            <li><p><m>h(x_2) - h(x_1)</m></p></li>
            <li><p><m>\dfrac{h(x_2) - h(x_1)}{x_2 - x_1} </m></p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="54"><statement><p>
        <ol label="a">
            <li><p><m>\Delta y</m> as <m>x</m> increases from <m>2</m> to <m>2+h</m></p></li>
            <li><p>The slope of the line segment joining <m>P</m> to <m>Q</m></p></li>
        </ol>
        <image source="images/fig-chap1-rev-54"  width="70%">
          <description>
            piecewise linear function f
          </description>
        </image>
    </p></statement>
    <answer><p>
        <ol label="a">
            <li><p><m>h(x_2) - h(x_1)</m></p></li>
            <li><p><m>\dfrac{h(x_2) - h(x_1)}{x_2 - x_1} </m></p></li>
        </ol>
    </p></answer>
    </exercise>
</exercisegroup>

<exercisegroup cols="2"><introduction><p>Which of the following tables could represent linear functions?</p></introduction>
    <exercise number="55"><statement><p>
        <ol label="a" cols="2">
            <li><p>
                <sidebyside><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>r</m></cell>
                        <cell><m>E</m></cell>
                    </row>
                    <row>
                        <cell><m>1</m></cell>
                        <cell><m>5</m></cell>
                    </row>
                    <row>
                        <cell><m>2</m></cell>
                        <cell><m>\frac{5}{2}</m></cell>
                    </row>
                    <row>
                        <cell><m>3</m></cell>
                        <cell><m>\frac{5}{3}</m></cell>
                    </row>
                    <row>
                        <cell><m>4</m></cell>
                        <cell><m>\frac{5}{4}</m></cell>
                    </row>
                    <row>
                        <cell><m>5</m></cell>
                        <cell><m>1</m></cell>
                    </row>
                </tabular></sidebyside>
            </p></li>
            <li><p>
                <sidebyside><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>s</m></cell>
                        <cell><m>t</m></cell>
                    </row>
                    <row>
                        <cell><m>10</m></cell>
                        <cell><m>6.2</m></cell>
                    </row>
                    <row>
                        <cell><m>20</m></cell>
                        <cell><m>9.7</m></cell>
                    </row>
                    <row>
                        <cell><m>30</m></cell>
                        <cell><m>12.6</m></cell>
                    </row>
                    <row>
                        <cell><m>40</m></cell>
                        <cell><m>15.8</m></cell>
                    </row>
                    <row>
                        <cell><m>50</m></cell>
                        <cell><m>19.0</m></cell>
                    </row>
                </tabular></sidebyside>
            </p></li>
        </ol>
    </p></statement>
    <answer><p>Neither</p></answer>
    </exercise>
    <exercise number="56"><statement><p>
        <ol label="a" cols="2">
            <li><p>
                <sidebyside><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>w</m></cell>
                        <cell><m>A</m></cell>
                    </row>
                    <row>
                        <cell><m>2</m></cell>
                        <cell><m>-13</m></cell>
                    </row>
                    <row>
                        <cell><m>4</m></cell>
                        <cell><m>-23</m></cell>
                    </row>
                    <row>
                        <cell><m>6</m></cell>
                        <cell><m>-33</m></cell>
                    </row>
                    <row>
                        <cell><m>8</m></cell>
                        <cell><m>-43</m></cell>
                    </row>
                    <row>
                        <cell><m>10</m></cell>
                        <cell><m>-53</m></cell>
                    </row>
                </tabular></sidebyside>
            </p></li>
            <li><p>
                <sidebyside><tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
                    <row>
                        <cell><m>x</m></cell>
                        <cell><m>C</m></cell>
                    </row>
                    <row>
                        <cell><m>0</m></cell>
                        <cell><m>0</m></cell>
                    </row>
                    <row>
                        <cell><m>2</m></cell>
                        <cell><m>5</m></cell>
                    </row>
                    <row>
                        <cell><m>4</m></cell>
                        <cell><m>10</m></cell>
                    </row>
                    <row>
                        <cell><m>8</m></cell>
                        <cell><m>20</m></cell>
                    </row>
                    <row>
                        <cell><m>16</m></cell>
                        <cell><m>40</m></cell>
                    </row>
                </tabular></sidebyside>
            </p></li>
        </ol>
    </p></statement>
    </exercise>

</exercisegroup>

<exercisegroup cols="2"><introduction><p>Each table gives values for a linear function. Fill in the missing values.</p></introduction>

    <exercise number="57"><statement><p>
        <tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
            <row>
                <cell><m>d</m></cell>
                <cell><m>V</m></cell>
            </row>
            <row>
                <cell><m>-5</m></cell>
                <cell><m>-4.8</m></cell>
            </row>
            <row>
                <cell><m>-2</m></cell>
                <cell><m>-3</m></cell>
            </row>
            <row>
                <cell><m></m></cell>
                <cell><m>-1.2</m></cell>
            </row>
            <row>
                <cell><m>6</m></cell>
                <cell><m>1.8</m></cell>
            </row>
            <row>
                <cell><m>10</m></cell>
                <cell><m></m></cell>
            </row>
        </tabular>
    </p></statement>
    <answer><p>
        <tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
            <row>
                <cell><m>d</m></cell>
                <cell><m>V</m></cell>
            </row>
            <row>
                <cell><m>-5</m></cell>
                <cell><m>-4.8</m></cell>
            </row>
            <row>
                <cell><m>-2</m></cell>
                <cell><m>-3</m></cell>
            </row>
            <row>
                <cell><m>\alert{1}</m></cell>
                <cell><m>-1.2</m></cell>
            </row>
            <row>
                <cell><m>6</m></cell>
                <cell><m>1.8</m></cell>
            </row>
            <row>
                <cell><m>10</m></cell>
                <cell><m>\alert{4.2} </m></cell>
            </row>
        </tabular>
    </p></answer>
    </exercise>

    <exercise number="58"><statement><p>
        <tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
            <row>
                <cell><m>q</m></cell>
                <cell><m>S</m></cell>
            </row>
            <row>
                <cell><m>-8</m></cell>
                <cell><m>-8</m></cell>
            </row>
            <row>
                <cell><m>-4</m></cell>
                <cell><m>56</m></cell>
            </row>
            <row>
                <cell><m>3</m></cell>
                <cell><m></m></cell>
            </row>
            <row>
                <cell><m></m></cell>
                <cell><m>200</m></cell>
            </row>
            <row>
                <cell><m>9</m></cell>
                <cell><m></m></cell>
            </row>
        </tabular>
    </p></statement>
    </exercise>

</exercisegroup>

<exercisegroup cols="2"><introduction><p>Find the slope and <m>y</m>-intercept of each line.</p></introduction>

    <exercise number="59"><statement><p><m>2x - 4y = 5</m></p></statement>
    <answer><p><m>m = \dfrac{1}{2}, ~b =\dfrac{-5}{4}</m></p></answer>
    </exercise>

    <exercise number="60"><statement><p><m>\dfrac{1}{2}x + \dfrac{2}{3}y = \dfrac{5}{6}</m></p></statement>
    </exercise>

    <exercise number="61"><statement><p><m>8.4x + 2.1y = 6.3</m></p></statement>
    <answer><p><m>m = -4, ~b = 3</m></p></answer>
    </exercise>

    <exercise number="62"><statement><p><m>y - 3 = 0</m></p></statement>
    </exercise>

</exercisegroup>


<exercisegroup cols="2"><introduction><p>For Problems 63 and 64,
    <ol label="a">
        <li><p>Graph by hand the line that passes through the given point with the given slope.</p></li>
        <li><p>Find an equation for the line.</p></li>
    </ol>
    </p></introduction>

    <exercise number="63"><statement><p><m>(-4, 6)</m>; <m>m =\dfrac{-2}{3}</m></p></statement>
    <answer><p>
    <ol label="a" cols="2">
        <li><p><image source="images/fig-ans-chap1-rev-63"  width="80%"><description>line</description></image> </p></li>
        <li><p><m>y = \dfrac{10}{3}- \dfrac{2}{3}x</m></p></li>
    </ol>
    </p></answer>
    </exercise>

    <exercise number="64"><statement><p><m>(2, -5)</m>; <m>m =\dfrac{3}{2}</m></p></statement>
    </exercise>

</exercisegroup>


<exercisegroup cols="2"><introduction><p>For Problems 65 and 66,
    <ol label="a">
        <li><p>Find the slope and <m>y</m>-intercept of each line.</p></li>
        <li><p>Write an equation for the line.</p></li>
    </ol>
    </p></introduction>

    <exercise number="65"><statement><p><image source="images/fig-chap1-rev-65"  width="70%"><description>line</description></image>
    </p></statement>
    <answer><p>
    <ol label="a" cols="2">
        <li><p><m>m = -2, ~b = 3</m> </p></li>
        <li><p><m>y = 3 - 2x</m></p></li>
    </ol>
    </p></answer>
    </exercise>

    <exercise number="66"><statement><p><image source="images/fig-chap1-rev-66"  width="70%"><description>line</description></image></p></statement>
    </exercise>

</exercisegroup>

    <exercise number="67"><statement><p>What is the slope of the line whose intercepts are <m>(-5, 0)</m> and <m>(0, 3)</m>?</p></statement>
    <answer><p><m>\dfrac{3}{5} </m></p></answer>
    </exercise>

    <exercise number="68"><statement><p>
        <ol label="a">
            <li><p>Find the <m>x</m>- and <m>y</m>-intercepts of the line <m>\dfrac{x}{4}- \dfrac{y}{6}= 1</m>.</p></li>
            <li><p>What is the slope of the line in part (a)?</p></li>
        </ol>
    </p></statement>
    </exercise>

    <exercise number="69"><statement><p>
        <ol label="a">
            <li><p>What is the slope of the line <m>y = 2 + \dfrac{3}{2}(x - 4)</m>?</p></li>
            <li><p>Find the point on the line whose <m>x</m>-coordinate is <m>4</m>. Can there be more than one such point?</p></li>
            <li><p>Use your answers from parts (a) and (b) to find another point on the line.</p></li>
        </ol>
    </p></statement>
    <answer><p>
        <ol label="a" cols="3">
            <li><p><m>\dfrac{3}{2} </m></p></li>
            <li><p><m>(4,2)</m>, no</p></li>
            <li><p><m>(6,5)</m></p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="70"><statement><p>A line passes through the point <m>(-2, -6)</m> and has slope <m>\dfrac{2}{3} </m>. Find the coordinates of two more points on the line.</p></statement>
    </exercise>

    <exercise number="71"><statement><p>A line passes through the point <m>(-5, 3)</m> and has slope <m>-\dfrac{8}{5} </m>. Find the coordinates of two more points on the line.</p></statement>
    <answer><p><m>(3,-14), ~(-7, 2)</m></p></answer>
    </exercise>

    <exercise number="72"><statement><p>Find an equation in point-slope form for the line of slope <m>\dfrac{6}{5}</m> that passes through <m>(-3, -4)</m>.</p></statement>
    </exercise>

    <exercise number="73"><statement><p>The rate at which air temperature decreases with altitude is called the lapse rate. In the troposphere, the layer of atmosphere that extends from the Earth’s surface to a height of about <m>7</m> miles, the lapse rate is about <m>3.6\degree</m>F for every <m>1000</m> feet. (Source: Ahrens, 1998)
    <ol label="a">
        <li><p>If the temperature on the ground is <m>62\degree</m>F, write an equation for the temperature, <m>T</m>, at an altitude of <m>h</m> feet.</p></li>
        <li><p>What is the temperature outside an aircraft flying at an altitude of <m>30,000</m> feet? How much colder is that than the ground temperature?</p></li>
        <li><p>What is the temperature at the top of the troposphere?</p></li>
    </ol>
    </p></statement>
    <answer><p>
    <ol label="a" cols="3">
        <li><p><m>T = 62 - 0.0036h</m></p></li>
        <li><p><m>-46\degree</m>F; <m>108\degree</m>F</p></li>
        <li><p><m>-71\degree</m>F</p></li>
    </ol>
    </p></answer>
    </exercise>

    <exercise number="74"><statement><p>In his television program <booktitle>Notes from a Small Island</booktitle>, aired in February 1999, Bill Bryson discussed the future of the British aristocracy. Because not all families produce an heir, 4 or 5 noble lines die out each year. At this rate, Mr. Bryson says, if no more peers are created, there will be no titled families left by the year 2175.
    <ol label="a">
        <li><p>Assuming that on average <m>4.5</m> titled families die out each year, write an equation for the number, <m>N</m>, of noble houses left in year <m>t</m>, where <m>t = 0</m> in the year 1999.</p></li>
        <li><p>Graph your equation.</p></li>
        <li><p>According to your graph, how many noble families existed in 1999? Which point on the graph corresponds to this information?</p></li>
    </ol>
    </p></statement>
    </exercise>


<exercisegroup cols="2"><introduction><p>Find an equation for the line passing through the two given points.</p></introduction>

    <exercise number="75"><statement><p><m>(3, -5), ~(-2, 4)</m></p></statement>
    <answer><p><m>y = \dfrac{2}{5}- \dfrac{9}{5}x</m></p></answer>
    </exercise>

    <exercise number="76"><statement><p><m>(0, 8), ~(4, -2)</m></p></statement>
    </exercise>

</exercisegroup>


<exercisegroup ><introduction><p>For Problems 77 and 78,
    <ol label="a">
        <li><p>Make a table of values showing two data points.</p></li>
        <li><p>Find a linear equation relating the variables.</p></li>
        <li><p>State the slope of the line, including units, and explain its meaning in the context of the problem.</p></li>
    </ol>
    </p></introduction>

    <exercise number="77"><statement><p>
        The population of Maple Rapids was <m>4800</m> in 1990 and had grown to <m>6780</m> by 2005. Assume that the population increases at a constant rate. Express the population, <m>P</m>, of Maple Rapids in terms of the number of years, <m>t</m>, since 1990.
    </p></statement>
    <answer><p>
        <ol label="a">
            <li><p>
                <tabular top="major" halign="center" right="minor" left="minor" bottom="minor">
                    <row bottom="minor">
                        <cell><m>t</m></cell>
                        <cell><m>0</m></cell>
                        <cell><m>15</m></cell>
                    </row>
                    <row>
                        <cell><m>P</m></cell>
                        <cell><m>4800</m></cell>
                        <cell><m>6780</m></cell>
                    </row>
                </tabular>
            </p></li>
            <li><p><m>P = 4800 + 132t</m></p></li>
            <li><p><m>m = 132</m> people/year: the population grew at a rate of <m>132</m> people per year.</p></li>
        </ol>
    </p></answer>
    </exercise>

    <exercise number="78"><statement><p>
        Cicely’s odometer read <m>112</m> miles when she filled up her <m>14</m>-gallon gas tank and <m>308</m> when the gas gauge read half full. Express her odometer reading, <m>m</m>, in terms of the amount of gas, <m>g</m>, she used
    </p></statement>
    </exercise>

</exercisegroup>
   
<exercise number="79"><statement><p>
   In 1986, the space shuttle Challenger exploded because of O-ring failure on a morning when the temperature was about <m>30\degree</m>F. Previously, there had been one incident of O-ring failure when the temperature was <m>70\degree</m>F and three incidents when the temperature was <m>54\degree</m>F. Use linear extrapolation to estimate the number of incidents of O-ring failure you would expect when the temperature is <m>30\degree</m>F.
</p></statement>
<answer><p><m>6</m></p></answer>
</exercise> 

<exercise number="80"><statement><p>
   Thelma typed a <m>19</m>-page technical report in <m>40</m> minutes. She required only <m>18</m> minutes for an <m>8</m>-page technical report. Use linear interpolation to estimate how long Thelma would require to type a <m>12</m>-page technical report.
</p></statement>
</exercise> 

<exercise number="81"><statement><p>
    The scatterplot shows weights (in pounds) and heights (in inches) for a team of distance runners.
    <image source="images/fig-chap1-rev-81"  width="25%">
      <description>
        scatterplot of weight vs height
      </description>
    </image>
    <ol label="a">
        <li><p>Use a straightedge to draw a line that fits the data.</p></li>
        <li><p>Use your line to predict the weight of a <m>65</m>-inch-tall runner and the weight of a <m>71</m>-inch-tall runner.</p></li>
        <li><p>Use your answers from part (b) to approximate the equation of a regression line.</p></li>
        <li><p>Use your answer to part (c) to predict the weight of a runner who is <m>68</m> inches tall.</p></li>
        <li><p>The points on the scatterplot are <m>(65.5, 130)</m>, <m>(66.5, 133)</m>, <m>(67, 135)</m>, <m>(69, 140)</m>, and <m>(70, 143)</m>. Use your calculator to find the least squares regression line.</p></li>
        <li><p>Use the regression line to predict the weight of a runner who is <m>68</m> inches tall.</p></li>
    </ol>
    </p></statement>
    <answer><p>
    <ol label="a" cols="2">
        <li><p><image source="images/fig-ans-chap1-rev-81"  width="50%"><description>scatterplot with regression line</description></image> </p></li>
        <li><p><m>129</m> lb, <m>145</m> lb</p></li>
        <li><p><m>y = 2.\overline{6} x - 44.\overline{3}</m></p></li>
        <li><p><m>137</m> lb</p></li>
        <li><p><m>y=2.84x - 55.74</m></p></li>
        <li><p><m>137.33</m> lb</p></li>
    </ol>
    </p></answer>
</exercise>

<exercise number="82"><statement><p>
    The scatterplot shows best times for various women running 400 meters and 100 meters.
    <image source="images/fig-chap1-rev-82"  width="30%">
      <description>
        scatterplot of 400 m vs 100m times
      </description>
    </image>
    <ol label="a">
        <li><p>Use a straightedge to draw a line that fits the data.</p></li>
        <li><p>Use your line to predict the 400-meter time of a woman who runs the 100-meter dash in <m>11.2</m> seconds and the 400-meter time of a woman who runs the 100-meter dash in <m>13.2</m> seconds.</p></li>
        <li><p>Use your answers from part (b) to approximate the equation of a regression line.</p></li>
        <li><p>Use your answer to part (c) to predict the 400-meter time of a woman who runs the 100-meter dash in <m>12.1</m> seconds.</p></li>
        <li><p>The points on the scatterplot are <m>(11.1, 52.4)</m>, <m>(11.5, 54.7)</m>, <m>(11.9, 57.4)</m>, <m>(12.2, 57.9)</m>, <m>(12.7, 61.3)</m>, and <m>(13.0, 63.0)</m>. Use your calculator to find the least squares regression line.</p></li>
        <li><p>Use the regression line to predict the 400-meter time of a woman who runs the 100-meter dash in <m>12.1</m> seconds.</p></li>
    </ol>
    </p></statement>
</exercise>

<exercise number="83"><statement><p>
    <term>Archaeopteryx</term> is an extinct creature with characteristics of both birds and reptiles. Only six fossil specimens are known, and only five of those include both a femur (leg bone) and a humerus (forearm bone) The scatterplot shows the lengths of femur and humerus for the five Archaeopteryx specimens.
    <image source="images/fig-chap1-rev-83"  width="30%">
      <description>
        scatterplot of femur vs humerus
      </description>
    </image>
    <ol label="a">
        <li><p>Use a straightedge to draw a line that fits the data.</p></li>
        <li><p>Predict the humerus length of an Archaeopteryx whose femur is <m>40</m> centimeters</p></li>
        <li><p>Predict the humerus length of an Archaeopteryx whose femur is <m>75</m> centimeters</p></li>
        <li><p>Use your answers from parts (b) and (c) to approximate the equation of a regression line.</p></li>
        <li><p>Use your answer to part (d) to predict the humerus length of an Archaeopteryx whose femur is <m>60</m> centimeters.</p></li>
        <li><p>Use your calculator and the given points on the scatterplot to find the least squares regression line. Compare the score this equation gives for part (d) with what you predicted earlier. The ordered pairs defining the data are <m>(38, 41)</m>, <m>(56, 63)</m>, <m>(59, 70)</m>, <m>(64, 72)</m>, <m>(74, 84)</m>.</p></li>
    </ol>
    </p></statement>
    <answer><p>
    <ol label="a" cols="2">
        <li><p><image source="images/fig-ans-chap1-rev-83"  width="75%"><description>scatterplot with regression line</description></image> </p></li>
        <li><p><m>45</m> cm</p></li>
        <li><p><m>87</m> cm</p></li>
        <li><p><m>y = 1.2x - 3</m></p></li>
        <li><p><m>69</m> cm</p></li>
        <li><p><m>y = 1.197x - 3.660</m>; <m>68.16</m> cm</p></li>
    </ol>
    </p></answer>
</exercise>

<exercise number="84"><statement><p>
    The scatterplot shows the boiling temperature of various substances on the horizontal axis and their heats of vaporization on the vertical axis. (The heat of vaporization is the energy needed to change the substance from liquid to gas at its boiling point.)
    <image source="images/fig-chap1-rev-84"  width="45%">
      <description>
        scatterplot of boiling point vs heat of vaporization
      </description>
    </image>
    <ol label="a">
        <li><p>Use a straightedge to estimate a line of best fit for the scatterplot.</p></li>
        <li><p>Use your line to predict the heat of vaporization of silver, whose boiling temperature is <m>2160\degree</m>C.</p></li>
        <li><p>Find the equation of the regression line.</p></li>
        <li><p>Use the regression line to predict the heat of vaporization of potassium bromide, whose boiling temperature is <m>1435\degree</m>C.</p></li>
    </ol>
    </p></statement>
</exercise>

</exercises>