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<h4>Meanings in Functions </h4>
<p>Review the following examples to help you gain a better understanding of meanings in functions. </p>
<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>
<p><strong>Example 1 </strong></p>
<p>The number of cubic yards of dirt, \(D\), needed to cover a garden with an area of \(a\) square feet is given by \(D=g(a)\).
<ol class="os-raise-noindent">
<li>A garden with area 5000 \(ft^2\) requires 50 \(yd^3\) of dirt. Express this information in terms of the function \(g\).</li>
</ol>
</p>
</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>
<strong>Solution:</strong> \(g(5000)=50\)
</p>
</div>
<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 the meaning of the statement \(g(100)=1\).</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>
<strong>Solution:</strong> The number of cubic yards of dirt required for a garden of 100 square feet is 1. <br>
</p>
</div>
<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><strong>Example 2</strong></p>
<p>Let \(f(t)\) be the number of ducks in a lake \(t\) years after 1990. Explain the meaning of each statement:</p>
<ol class="os-raise-noindent">
<li>\(f(5)=30\)<br>
</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>
<strong>Solution:</strong> In 1995 (5 years after 1990), there were 30 ducks in the lake.<br>
</p>
</div>
<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>\(f(10)=40\)</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>
<strong>Solution:</strong> In 2000 (10 years after 1990), there were 40 ducks in the lake.
</p>
</div>
<h4>Try It: Meanings in Functions</h4>
<p>The amount of garbage, \(G\), produced by a city with population \(p\) is given by \(G=f(p)\). \(G\) is measured in tons per week, and \(p\) is measured in thousands of people.</p>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="42b6f5df-e2c8-4109-83ef-a727cc0a3f11" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="1">
<li>The town of Tola has a population of 40,000 and produces 13 tons of garbage each week. Express this information in terms of the function \(f\).</li>
<p>Write down your answer. Then select the <strong>solution</strong> button to compare your work.
</p>
</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>\(13=f(40)\)</p>
</div>
</div>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="b1626ee9-b17e-44ba-b637-baadc52c489a" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>Explain the meaning of the statement \(f(5)=2\).</li>
<p>Write down your answer. Then select the <strong>solution</strong> button to compare your work.
</p>
</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>Five thousand people will produce 2 tons of garbage each week.</p>
</div>
</div>