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<h4>Matching Exponential Functions and Graphs</h4>
<p>For each of the following, match each function with one of the graphs in the picture below.</p>
<p><img alt="Graph of six exponential functions." class="img-fluid atto_image_button_text-bottom" height="295" role="presentation" src="https://k12.openstax.org/contents/raise/resources/13b36ed8389344dc587cabc989318f563a0a1795" width="300"></p>
<p>Remember, the equation for an exponential function is \(y=a\cdot b^x\). The \(a\) will affect the \(y\)-intercept. When \(b<1\), there is exponential decay. The closer \(b\) is to 0, the faster it decays. The closer \(b\) is to 1, the slower it decays. When \(b>1\), the larger the value of \(b\), the faster it grows.</p>
<table class="os-raise-wideadjustedtable">
<thead>
<tr>
<th scope="col">Equation</th>
<th scope="col">\(y\)-intercept</th>
<th scope="col">Growth/Decay</th>
<th scope="col">Match</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<ol class="os-raise-noindent">
<li>\(f(x)=2(0.68)^x\) </li>
</ol>
</td>
<td>
\((0, 2)\)
</td>
<td>
Decay
</td>
<td>
B
</td>
</tr>
<tr>
<td>
<ol class="os-raise-noindent" start="2">
<li>\(
f(x)=2(1.28)^x\) </li>
</ol>
</td>
<td>
\((0, 2)\)
</td>
<td>
Growth
</td>
<td>
F
</td>
</tr>
<tr>
<td>
<ol class="os-raise-noindent" start="3">
<li>\(
f(x)=2(0.81)^x\) </li>
</ol>
</td>
<td>
\((0, 2)\)
</td>
<td>
Decay
</td>
<td>
A
</td>
</tr>
<tr>
<td>
<ol class="os-raise-noindent" start="4">
<li>\( f(x)=4(1.28)^x\)</li>
</ol>
</td>
<td>
\((0, 4)\)
</td>
<td>
Growth
</td>
<td>
D
</td>
</tr>
<tr>
<td>
<ol class="os-raise-noindent" start="5">
<li>\(f(x)=2(1.59)^x\)</li>
</ol>
</td>
<td>
\((0, 2)\)
</td>
<td>
Growth
</td>
<td>
E
</td>
</tr>
<tr>
<td>
<ol class="os-raise-noindent" start="6">
<li>\(f(x)=4(0.68)^x\)</li>
</ol>
</td>
<td>
\((0, 4)\)
</td>
<td>
Decay
</td>
<td>
C
</td>
</tr>
</tbody>
</table>
<br>
<h4> Try It: Matching Exponential Functions and 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><img alt="Graph of six exponential functions." height="295" src="https://k12.openstax.org/contents/raise/resources/a3588f5079a44777c05412324d2a3176b0b499d5" width="300"></p>
<p>In the graph above, which function, \(f(x)=a \cdot b^x\), has the largest value for \(a\)?</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 answer:</p>
<p>Here is how to identify which has the largest value for \(a\):</p>
<p>In the function \(f(x)=a \cdot b^x\), \(a\) changes the \(y\)-intercept. The function with the largest \(y\)-intercept is C. It crosses the \(y\)-axis at the highest point.</p>
</div>