0306ec90-5867-4f60-bc5b-34ceeaa5c260.html

<h4>Cool Down Activity</h4>
<p>Examine the three graphs representing three exponential functions: \(f\), \(g\), and \(h\).</p>
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<p><img alt role="presentation" src="https://k12.openstax.org/contents/raise/resources/c91699a5862502edaffc0fc9cafd5d89472eebad" width="400"></p>
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<p>The functions \(f\) and \(h\) are defined as:</p>
<ul>
  <li>\(f(x)=10 \cdot 2^x\)</li>
  <li>\(h(x)=20 \cdot 4^x\)</li>
</ul>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="b6a65553-df6d-4524-a666-6848eb15aee5" data-retry-limit="0" data-schema-version="1.0">
  <div class="os-raise-ib-pset-problem" data-content-id="8349eeef-9ab1-4105-bcd7-065b0c411f0f" data-problem-type="multiplechoice" data-solution="\(g(x)=20 \cdot (2.5)^x\)" data-solution-options='["\\(g(x)=20 \\cdot (1.5)^x\\)", "\\(g(x)=20 \\cdot (2.5)^x\\)", "\\(g(x)=10 \\cdot (3.5)^x\\)", "\\(g(x)=20 \\cdot (4.5)^x\\)"]'>
    <div class="os-raise-ib-pset-problem-content">
      <ol class="os-raise-noindent">
        <li>Which of the following could define function \(g\)? Be prepared to show your reasoning.</li>
      </ol>
    </div>
    <div class="os-raise-ib-pset-correct-response">
      <p>Correct! </p>
    </div>
        <div class="os-raise-ib-pset-attempts-exhausted-response">
      <p>Nice try! The correct answer is \(g(x)=20 \cdot (2.5)^x\).
      </p>
    </div>
  </div>
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  <div class="os-raise-ib-pset-correct-response"> </div>
  <div class="os-raise-ib-pset-attempts-exhausted-response"> </div>
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<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
  <div class="os-raise-ib-cta-content">
    <ol class="os-raise-noindent" start="2">
      <li>Explain your reasoning.</li>
    </ol>
  </div>
  <div class="os-raise-ib-cta-prompt">
    <p>Write down your answer, then select the <strong>solution</strong> button to compare your work. </p>
  </div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
  <p>Compare your answer:</p>
  <p>The graph of \(g\)&nbsp;has the same \(y\)-intercept as the graph of \(h\), which is 20. It grows more quickly than \(f\)&nbsp;but more slowly than \(h\),<i>&nbsp;</i>so the growth factor must be greater than 2 but less than 4.</p>
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