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<h4>Activity</h4>
<p>For questions 1-6, use the following information to complete the table. Show the predicted number of downloads at each listed price. The first row has been completed for you.</p>
<blockquote>A company that sells movies online is deciding how much to charge customers to download a new movie. Based on data from previous sales, the company predicts that if they charge \(x\) dollars for each download, then the number of downloads, in thousands, is \(18-x\).</blockquote>
<table class="os-raise-wideequaltable">
<thead>
<tr>
<th scope="col">Price (dollars per download)</th>
<th scope="col">Number of downloads (thousands)</th>
<th scope="col">Revenue (thousands of dollars)</th>
</tr>
</thead>
<tbody>
<tr>
<td>
\(3\)
</td>
<td>
\(15\)
</td>
<td>
\(45\)
</td>
</tr>
<tr>
<td>
\(5\)
</td>
<td>
<ol class="os-raise-noindent">
<li> _____ </li>
</ol>
</td>
<td> </td>
</tr>
<tr>
<td>
\(10\)
</td>
<td>
<ol class="os-raise-noindent" start="2">
<li> _____ </li>
</ol>
</td>
<td> </td>
</tr>
<tr>
<td>
\(12\)
</td>
<td>
<ol class="os-raise-noindent" start="3">
<li> _____ </li>
</ol>
</td>
<td> </td>
</tr>
<tr>
<td>
\(15\)
</td>
<td>
<ol class="os-raise-noindent" start="4">
<li> _____ </li>
</ol>
</td>
<td> </td>
</tr>
<tr>
<td>
\(18\)
</td>
<td>
<ol class="os-raise-noindent" start="5">
<li> _____ </li>
</ol>
</td>
<td> </td>
</tr>
<tr>
<td>
\(x\)
</td>
<td>
<ol class="os-raise-noindent" start="6">
<li> _____ </li>
</ol>
</td>
<td> </td>
</tr>
</tbody>
</table>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="afde8053-f5c7-4390-a1be-c3afd1bca59c" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q1a-->
<div class="os-raise-ib-pset-problem" data-content-id="31235259-bc95-4698-b236-52c61d0a8525" data-problem-comparator="integer" data-problem-type="input" data-solution="13">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent">
<li> When the price is \($5\) per download, what is the number of downloads in thousands? </li>
</ol>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! There are \(13\) thousand downloads when the price is \($5\) per download.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p> Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(13\). There are \(13\) thousand downloads when the price is \($5\) per download.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1b-->
<div class="os-raise-ib-pset-problem" data-content-id="a4f04d9b-9922-4779-b613-60f9e71080a9" data-problem-comparator="integer" data-problem-type="input" data-solution="8">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2">
<li> When the price is \($10\) per download, what is the number of downloads in thousands? </li>
</ol>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! There are \(8,000\) downloads when the price is \($10\) per download.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p> Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(8\). There are \(8,000\) downloads when the price is \($10\) per download.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1c-->
<div class="os-raise-ib-pset-problem" data-content-id="0586c43d-779a-4e6b-bb60-9f543ef4b31d" data-problem-comparator="integer" data-problem-type="input" data-solution="6">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="3">
<li> When the price is \($12\) per download, what is the number of downloads in thousands? </li>
</ol>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! There are \(6,000\) downloads when the price is \($12\) per download.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p> Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(6\). There are \(6,000\) downloads when the price is \($12\) per download.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1d-->
<div class="os-raise-ib-pset-problem" data-content-id="3b858498-3a64-4358-8dc6-7268d8abf190" data-problem-comparator="integer" data-problem-type="input" data-solution="3">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="4">
<li> When the price is \($15\) per download, what is the number of downloads in thousands? </li>
</ol>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! There are \(3,000\) downloads when the price is \($15\) per download.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p> Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(3\). There are \(3,000\) downloads when the price is \($15\) per download.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1e-->
<div class="os-raise-ib-pset-problem" data-content-id="7aceacfd-a174-43be-8421-91a3be927b97" data-problem-comparator="integer" data-problem-type="input" data-solution="0">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="5">
<li> When the price is \($18\) per download, what is the number of downloads in thousands? </li>
</ol>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! There are \(0\) downloads when the price is \($18\) per download.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p> Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(0\). There are \(0\) downloads when the price is \($18\) per download.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div></div>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="57597289-146d-4a8f-acf4-410cad4d8d2f" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="6">
<li> When the price is \($x\) per download, what is the number of downloads in thousands? </li>
</ol>
</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>
\(18-x\)
</div>
</div>
<!--Interaction End -->
<br>
<p> For questions 7-12 complete the table by finding the <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">revenue</span> at each price. The first row has been completed for you.</p>
<br>
<table class="os-raise-wideequaltable">
<thead>
<tr>
<th scope="col">Price (dollars per download)</th>
<th scope="col">Number of downloads (thousands)</th>
<th scope="col">Revenue (thousands of dollars)</th>
</tr>
</thead>
<tbody>
<tr>
<td>
\(3\)
</td>
<td>
\(15\)
</td>
<td>
\(45\)
</td>
</tr>
<tr>
<td>
\(5\)
</td>
<td> </td>
<td>
<ol class="os-raise-noindent" start="7">
<li> _____ </li>
</ol>
</td>
</tr>
<tr>
<td>
\(10\)
</td>
<td> </td>
<td>
<ol class="os-raise-noindent" start="8">
<li> _____ </li>
</ol>
</td>
</tr>
<tr>
<td>
\(12\)
</td>
<td> </td>
<td>
<ol class="os-raise-noindent" start="9">
<li> _____ </li>
</ol>
</td>
</tr>
<tr>
<td>
\(15\)
</td>
<td> </td>
<td>
<ol class="os-raise-noindent" start="10">
<li> _____ </li>
</ol>
</td>
</tr>
<tr>
<td>
\(18\)
</td>
<td> </td>
<td>
<ol class="os-raise-noindent" start="11">
<li> _____ </li>
</ol>
</td>
</tr>
<tr>
<td>
\(x\)
</td>
<td> </td>
<td>
<ol class="os-raise-noindent" start="12">
<li> _____ </li>
</ol>
</td>
</tr>
</tbody>
</table>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="b7b6f3a2-8dfe-4cad-b9de-6a467eb2d6f3" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q1a-->
<div class="os-raise-ib-pset-problem" data-content-id="cc45646c-927c-45a7-87dc-f6a96a7f8579" data-problem-comparator="integer" data-problem-type="input" data-solution="65">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="7">
<li> When the price is \($5\) per download, what is the revenue in thousands of dollars? </li>
</ol>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The revenue is \($65,000\) when the price is \($5\) per download.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p> Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(65\). The revenue is \($65,000\) when the price is \($5\) per download.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1b-->
<div class="os-raise-ib-pset-problem" data-content-id="e7aaccfc-0240-497a-a0c9-ec861b2dda1c" data-problem-comparator="integer" data-problem-type="input" data-solution="80">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="8">
<li> When the price is \($10\) per download, what is the revenue in thousands of dollars? </li>
</ol>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The revenue is \($80,000\) when the price is \($10\) per download.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p> Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(80\). The revenue is \($80,000\) when the price is \($10\) per download.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1c-->
<div class="os-raise-ib-pset-problem" data-content-id="4e88c474-49f1-4712-b1dc-46b99de880c6" data-problem-comparator="integer" data-problem-type="input" data-solution="72">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="9">
<li> When the price is \($12\) per download, what is the revenue in thousands of dollars? </li>
</ol>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The revenue is \($72,000\) when the price is \($12\) per download.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p> Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(72\). The revenue is \($72,000\) when the price is \($12\) per download.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1d-->
<div class="os-raise-ib-pset-problem" data-content-id="bd176bc0-c793-43b2-b1b6-fd641dfb4775" data-problem-comparator="integer" data-problem-type="input" data-solution="45">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="10">
<li> When the price is \($15\) per download, what is the revenue in thousands of dollars? </li>
</ol>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The revenue is \($45,000\) when the price is \($15\) per download.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p> Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(45\). The revenue is \($45,000\) when the price is \($15.00\) per download.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1e-->
<div class="os-raise-ib-pset-problem" data-content-id="042887c7-c333-4cf5-bc62-0e91427afd6d" data-problem-comparator="integer" data-problem-type="input" data-solution="0">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="11">
<li> When the price is \($18\) per download, what is the revenue in thousands of dollars? </li>
</ol>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The revenue is \(0\) when the price is \($18\) per download.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p> Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(0\). The revenue is \(0\) when the price is \($18\) per download.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div></div>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="0b498f13-d637-41e1-89c1-eb493559dd49" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="12">
<li> When the price is \($x\) per download, what is the revenue in thousands of dollars? </li>
</ol>
</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> \(x(18-x)\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="dbd0afb2-df64-43bc-a312-4b91cff06f4a" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="13">
<li>Is the relationship between the price of the movie and the revenue (in thousands of dollars) linear, quadratic, or exponential? Explain how you know.</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: Your answer may vary, but here is a sample.</p>
<p>It is quadratic. The output \(x(18-x)\) can be written as \(18x-x^2\), which is a quadratic expression.</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--BEGIN ADD DESMOS INTERATIVE-->
<!--START QUESTION #14 -->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal87" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<!-- INSERT ANY VALID HTML HERE -->
<ol class="os-raise-noindent" start="14">
<li>Use the graphing tool or technology outside the course. Plot the points that represent the revenue, 𝑟, as a function of the price of one download in dollars, 𝑥, using the Desmos tool below. </li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>When you have finished graphing, select the <strong>solution</strong> button to compare your work. </p>
</div>
</div>
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<p>Compare your answer:</p>
<p><img alt="Grid with plotted points. X-axis labeled with price in dollars and \(y\)-axis labeled with revenue in thousands of dollars." height="247" src="https://k12.openstax.org/contents/raise/resources/f9c61c89cddcb41a1fa881b41d64fcd5e68b9d63" width="319"></p>
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<li>What price would you recommend the company charge for a new movie? Be prepared to show your reasoning.</li>
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<p>Enter your answer here:</p>
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<p>Compare your answer: Your answer may vary, but here is a sample.</p>
<p> Based on the graph, the largest revenue comes when the price is between \($5\) and \($10\). It is hard to tell exactly, but perhaps \($9\), halfway between \($0\) and \($18\).</p>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="38b0bacb-db13-4ea0-adda-162f526817a7" data-schema-version="1.0" data-wait-for-event="RFM1">
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<h4>Extending Your Thinking </h4>
<p>The function that uses the price (in dollars per download) \(x\) to determine the number of downloads (in thousands) \(18-x\) is an example of a demand function, and its graph is known. Economists are interested in factors that can affect the demand function and therefore the price suppliers wish to set.</p>
<ol class="os-raise-noindent" start="1">
<li>What are some things that could increase the number of downloads predicted for the same given prices?</li>
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<p>Enter your answer here:</p>
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<p>Compare your answer: Your answer may vary, but here is a sample.</p>
<p>The quality of the movies could improve. The number of people who like watching movies could increase. The price of watching a movie in a theater could go up.</p>
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<li>If the demand shifted so that we predicted \(20-x\) thousand downloads at a price of \(x\) dollars per download, what do you think would happen to the price that gives the maximum revenue? Check what actually happens.</li>
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<p>Enter your answer here:</p>
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<p>Compare your answer: Your answer may vary, but here is a sample.</p>
<p>The price that gives the maximum revenue would increase from \($9\) to \($10\).</p>
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