aa084809-eadc-4ae5-a25f-cd30e336613f.html

<h4>Cool Down Activity</h4>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="b8f265a9-aba5-45ad-9022-9304677fcaa2"
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  <div class="os-raise-ib-input-content">
    <p>Tyler completes the table comparing values of the expressions \(5x^2\) and \(2^x\).</p>
    <table class="os-raise-skinnytable">
      <thead>
        <tr>
          <th scope="col">\(x\)</th>
          <th scope="col">\(5x^2\)</th>
          <th scope="col">\(2^x\)</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>\(1\)</td>
          <td>\(5\)</td>
          <td>\(2\)</td>
        </tr>
        <tr>
          <td>\(2\)</td>
          <td>\(20\)</td>
          <td>\(4\)</td>
        </tr>
        <tr>
          <td>\(3\)</td>
          <td>\(45\)</td>
          <td>\(8\)</td>
        </tr>
        <tr>
          <td>\(4\)</td>
          <td>\(80\)</td>
          <td>\(16\)</td>
        </tr>
      </tbody>
    </table>
    <br>
    <p>Tyler concludes that \(5x^2\) will always result in greater values than \(2^x\) for the same value of \(x\). Do
      you agree? Explain or show your reasoning.</p>
  </div>
  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
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  <div class="os-raise-ib-input-ack">
    <p>Compare your answer:</p>
    <p>Tyler is not correct. For lesser values of \(x\), \(5x^2\) results in greater values than \(2^x\), but \(2^x\)
      eventually results in greater values because it always doubles when \(x\) increases by \(1\). When \(x=9\),
      \(5(9)^2=405\) and \(2^9=512\), so \(2^9\) is greater.</p>
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</div>
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