943bc677-b2a8-4ac7-8501-b0f5a8107cff.html

<h4>Comparing Populations</h4>
<p>Graphs are very useful for comparing two or more functions. Here are graphs of functions \(C\) and \(T\), which give
  the populations (in millions) of California and Texas in year \(x\).</p>
<p><img alt="A GRAPH THAT SHOWS THE POPULATION IN MILLIONS FROM 1900 TO 2010 FOR THE STATES OF CALIFORNIA AND TEXAS." src="https://k12.openstax.org/contents/raise/resources/127fe8074872a6c9489127ecd8679d6c4f86ec31"></p>
<br>
<table class="os-raise-wideequaltable">
  <thead>
    <tr>
      <th scope="col">What can we tell about the populations?</th>
      <th scope="col">How can we tell?</th>
      <th scope="col">How can we convey this with function notation? </th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>In the early 1900s, California had a smaller population than Texas.
      </td>
      <td>The graph of \(C\) is below the graph of \(T\) when \(x\)<em> </em>is 1900.
      </td>
      <td>\(C(1900)&lt;T(1900)\)
      </td>
    </tr>
    <tr>
      <td>Around 1935, the two states had the same population of about 5 million people.
      </td>
      <td>The graphs intersect at about \((1935, 5)\).
      </td>
      <td>\(C(1935)=5\) and <br>
        \(T(1935)=5\), and <br>
        \(C(1935)=T(1935)\)
      </td>
    </tr>
    <tr>
      <td>After 1935, California has had more people than Texas.
      </td>
      <td>When \(x\) is greater than 1935, the graph of \(C(x)\) is above that of \(T(x)\).
      </td>
      <td>\(C(x)&gt;T(x)\) for<br>
        \(x&gt;1935\)
      </td>
    </tr>
    <tr>
      <td>Both populations have increased over time, with no periods of decline.
      </td>
      <td>Both graphs slant upward from left to right.
      </td>
      <td>&nbsp;</td>
    </tr>
    <tr>
      <td>From 1900 to 2010, the population of California has risen faster than that of Texas. California had a
        greater average rate of change.
      </td>
      <td>If we draw a line to connect the points for 1900 and 2010 on each graph, the line for <em>C</em> has a
        greater slope than that for <em>T</em>.
      </td>
      <td>\(\frac{C(2010)-C(1900)}{201-1900}&gt;\frac{T(2010)-T(1900)}{2010-1900}\)
      </td>
    </tr>
  </tbody>
</table>
<br>
<h4>Try It: Comparing Populations</h4>
<br>
<p>Examine the graph given above that displays the populations of California and Texas over time.</p>


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   <div class="os-raise-ib-pset-problem" data-problem-type="dropdown" data-solution="Texas" data-solution-options='["California", "Texas"]'>
         <div class="os-raise-ib-pset-problem-content">
          <ol class="os-raise-noindent">
            <li>Which state had a greater population in 1920?</li>
          </ol>               
          </div>
          <div class="os-raise-ib-pset-correct-response">
                <p>Correct! Texas.</p>
          </div>
          <div class="os-raise-ib-pset-encourage-response">
               <p>Try Again.</p>
          </div>
          <div class="os-raise-ib-pset-attempts-exhausted-response">
               <p>The correct answer is Texas.</p>
           </div>
    </div>
    <!--END QUESTION.-->

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      <div class="os-raise-ib-pset-encourage-response">
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="2c64f5e2-2ffb-4d03-9ff9-9cb805709212" data-fire-event="eventShow" data-schema-version="1.0">
  <div class="os-raise-ib-input-content">
    <ol class="os-raise-noindent" start="2">
      <li>Write a true mathematical statement using function notation to describe which state has the greater population in 1920.</li>
    </ol>
  </div>
  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
  </div>
  <div class="os-raise-ib-input-ack">
    <p>Compare your answer:</p>
    <p>\(C(1920)\;\lt\;T(1920)\)</p>
  </div>
</div>