7b0f6075-e3cc-4f3d-ad37-454862277bd8.html

<h4> Writing Functions from Graphs</h4>
<p><img
    alt="GRAPH OF AN EXPONENTIAL GROWTH FUNCTION. THE GRAPH PASSES THROUGH THE POINTS 0 COMMA 4, 1 COMMA 12, AND 2 COMMA 36."
    src="https://k12.openstax.org/contents/raise/resources/f5b8e4ad98579e421c915d6944c68bd1c9524248" width="300"></p>
<p>Find the equation of the function graphed above. Then find the value at \(f(5)\).</p>
<table class="os-raise-horizontaltable">
  <thead></thead>
  <tbody>
    <tr>
      <th scope="row">
        <ol class="os-raise-noindent">
          <li> Find the value of \(a\), the starting point. </li>
        </ol>
      </th>
      <td>
        \(a=4\)
      </td>
    </tr>
    <tr>
      <th scope="row">
        <ol class="os-raise-noindent" start="2">
          <li> Find the \(b\), the growth factor. </li>
        </ol>
      </th>
      <td>
        \(b=3\)
      </td>
    </tr>
    <tr>
      <th scope="row">
        <ol class="os-raise-noindent" start="3">
          <li> Write the equation of the function. </li>
        </ol>
      </th>
      <td>
        \(f(x)=4 \cdot 3^x\)
      </td>
    </tr>
    <tr>
      <th scope="row">
        <ol class="os-raise-noindent" start="4">
          <li> Find \(f(5)\). </li>
        </ol>
      </th>
      <td>
        \(f(5)=4 \cdot 3^5=972\)
      </td>
    </tr>
  </tbody>
</table>
<br>
<h4> Try It: Writing Functions from Graphs</h4>
<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">
    <p>Use the graph below to write the equation of the function. Then find \(f(5)\).</p>
    <p><img
        alt="GRAPH OF AN EXPONENTIAL GROWTH FUNCTION. THE GRAPH PASSES THROUGH THE POINTS 0 COMMA 2, 1 COMMA 8, AND 2 COMMA 32."
        src="https://k12.openstax.org/contents/raise/resources/c6886dff32bbb16d44b05f5c51a3a9d21993da87" width="300">
    </p>
  </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 answers:</p>
  <p>Here is how to write the exponential function from the graph:</p>
  <table class="os-raise-horizontaltable">
    <thead></thead>
    <tbody>
      <tr>
        <th scope="row">
          <ol class="os-raise-noindent">
            <li> Find the value of \(a\), the starting point. </li>
          </ol>
        </th>
        <td>
          \(a=2\)
        </td>
      </tr>
      <tr>
        <th scope="row">
          <ol class="os-raise-noindent" start="2">
            <li> Find the \(b\), the growth factor. </li>
          </ol>
        </th>
        <td>
          \(b=4\)
        </td>
      </tr>
      <tr>
        <th scope="row">
          <ol class="os-raise-noindent" start="3">
            <li> Write the equation of the function. </li>
          </ol>
        </th>
        <td>
          \(f(x)=2 \cdot 4^x\)
        </td>
      </tr>
      <tr>
        <th scope="row">
          <ol class="os-raise-noindent" start="4">
            <li> Find \(f(5)\). </li>
          </ol>
        </th>
        <td>
          \(f(x)=2 \cdot 4^5=2048\)
        </td>
      </tr>
    </tbody>
  </table>

</div>