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<h4>Activity</h4>
<p>A marine biologist estimates that a structure of coral has a volume of 1,200 cubic centimeters and that its volume
doubles each year.</p>
<p><img height="300" src="https://k12.openstax.org/contents/raise/resources/915e980323c039f033c1086572a5d1f032cef8c3" width="300"></p>
<br>
<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">
<li>Write an equation of the form \(y=a\cdot b^t\) representing the relationship, where \(t\) is time in
years since the coral was measured and \(y\) is volume of coral in cubic centimeters. (You need to figure
out what numbers \(a\) and \(b\) are in this situation.)</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>\(y=1,200\cdot 2^t\)</p>
</div>
<br>
<ol class="os-raise-noindent" start="2">
<li>Find the volume of the coral when \(t\) is 5, 1, 0, –1, and –2. Note that when \(t = -1\), this
represents one year before the marine biologist made the original estimate.<br>
</li>
</ol>
<table class="os-raise-horizontaltable">
<thead></thead>
<tbody>
<tr>
<th scope="row">Time (years)</th>
<td>5</td>
<td>1</td>
<td>0</td>
<td>-1</td>
<td>-2</td>
</tr>
<tr>
<th scope="row">Volume of Coral (cubic centimeters)</th>
<td>a.____
</td>
<td>b.____
</td>
<td>c.____
</td>
<td>d.____
</td>
<td>e.____
</td>
</tr>
</tbody>
</table>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="485289d3-90ab-487d-ba23-6eb8a3238bf3" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<div class="os-raise-ib-pset-problem" data-content-id="58888de2-7d9b-405d-a5bb-e1757fd262c3" data-problem-comparator="integer" data-problem-type="input" data-solution="3800">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" type="a">
<li> Enter the volume of coral when t = 5. Do not enter commas in your answer. </li>
</ol>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 3800 cubic centimeters</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 3800 cubic centimeters</p>
</div>
</div>
<div class="os-raise-ib-pset-problem" data-content-id="48eecec1-7ae0-48d7-8d2d-912f221f88f8" data-problem-comparator="integer" data-problem-type="input" data-solution="2400">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2" type="a">
<li> Enter the volume of coral when t = 1. Do not enter commas in your answer. </li>
</ol>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 2400 cubic centimeters</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 2400 cubic centimeters</p>
</div>
</div>
<div class="os-raise-ib-pset-problem" data-content-id="ec7943f4-d9f7-430c-86f7-b965ddc0b967" data-problem-comparator="integer" data-problem-type="input" data-solution="1200">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="3" type="a">
<li> Enter the volume of coral when t = 0. Do not enter commas in your answer. </li>
</ol>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 1200 cubic centimeters</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 1200 cubic centimeters</p>
</div>
</div>
<div class="os-raise-ib-pset-problem" data-content-id="d325a246-3666-4e89-87ff-f46f511a3cb8" data-problem-comparator="integer" data-problem-type="input" data-solution="600">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="4" type="a">
<li> Enter the volume of coral when t = -1. Do not enter commas in your answer. </li>
</ol>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 600 cubic centimeters</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 600 cubic centimeters</p>
</div>
</div>
<div class="os-raise-ib-pset-problem" data-content-id="839cb86e-da3a-45fc-9279-ca3b5bc704a5" data-problem-comparator="integer" data-problem-type="input" data-solution="300">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="5" type="a">
<li> Enter the volume of coral when t = -2. Do not enter commas in your answer. </li>
</ol>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 300 cubic centimeters</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 300 cubic centimeters</p>
</div>
</div>
<!--Do not edit below this line-->
<div class="os-raise-ib-pset-correct-response"> </div>
<div class="os-raise-ib-pset-attempts-exhausted-response"> </div>
</div>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="a279dee3-1ef1-44ac-8898-560fb004114a" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>What does it mean, in this situation, when \(t\) is –2?</li>
</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> This represents the time 2 years before the scientist made the estimate of 1,200 cubic centimeters.</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="334f0620-d6a6-417c-b671-2eae1b10f7df" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>In a certain year, the volume of the coral is 37.5 cubic centimeters. Which year is this? Be prepared to show
your reasoning.</li>
</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>\(t\) is –5, or 5 years before the scientist made the estimate of 1,200 cubic centimeters.</p>
</div>
</div>
<!--Interaction End -->