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794128af-1319-4883-a268-0c1d9af97efa.html
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<h4>Activity </h4>
<p>Here are graphs showing how the amount of money in each of the purses change. Remember, Purse A starts with $1,000 and grows by $200 each day. Purse B starts with $0.01 and doubles each day.</p>
<p><img alt="Graph of an exponential function, origin O. number of days and amount in dollar." class="img-fluid atto_image_button_text-bottom" height="186" src="https://k12.openstax.org/contents/raise/resources/728c20d8311a5f32ef4aba9fc24217f0d41c30cf" width="600"></p>
<br>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="badd3303-8b86-40e2-a373-ef7c851931ea" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>Which data on the graph shows the amount of money in Purse \(A\)? Which data on the graph shows the amount of money in Purse \(B\)? 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:</p>
<p>The blue data on the graph containing \(P\) is Purse \(B\), and the red data on the graph containing \(Q\) is Purse \(A\). Purse \(B\) starts with less money than Purse \(A\), so its graph will be lower at the beginning.The blue data on the graph containing \(P\) is Purse \(B\), and the red data on the graph containing \(Q\) is Purse \(A\). Purse \(B\) starts with less money than Purse \(A\), so its graph will be lower at the beginning. </p>
</div>
</div>
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<br>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d1bf07ee-91bb-4b2e-b1e7-098e384ce98e" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li> Points \(P\) and \(Q\) are labeled on the graph. Explain what they mean in terms of the genie’s offer. </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> Point \(P\) says that 9 days after the genie has appeared, Purse B contains $5.12. Point \(Q\) says that 5 days after the genie has appeared, Purse A contains $2,000. </p>
</div>
</div>
<!--Interaction End -->
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<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d2bbf4b9-bc97-4159-92f0-c0d8350665b5" 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 are the coordinates of the vertical intercept for each graph? 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:</p>
<p> For Purse A, the vertical intercept is \((0,1,000)\) because when the genie appears (day 0), the purse has $1,000. For Purse B, the vertical intercept is \((0,0.01)\) because it only contains $0.01 when the genie appears. </p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="2cd73032-490e-4ccc-881b-b2cff84c8916" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li> When does Purse B become a better choice than Purse A? 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> According to the graphs, on day 19 and afterward, Purse B is worth more than Purse A. This can be seen on the graph since Purse B has a greater \(y\)-coordinate for the first time when \(x\) is 19. </p>
</div>
</div>
<!--Interaction End -->
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<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="0f6f808b-df8e-4965-9c6e-1fc5e19af9f0" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li> Knowing what you know now, which purse would you choose? 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> Your answer may vary, but here is a sample: <br>
Purse \(B\) is worth more after 19 days, but there may be other considerations to take into account.</p>
</div>
</div>
<!--Interaction End -->
<br>
<p>While on a beach, your friend discovers a different genie. This genie also offers two purses to choose from, and he gives you the following graph to show how the money in each purse will grow. The set of triangular marks that lie on a line represent values in Purse A, and the set of square marks that make a curve represent those in Purse B.</p>
<p><img alt="Graph of 2 functions on grid." class="img-fluid atto_image_button_text-bottom" height="162" src="https://k12.openstax.org/contents/raise/resources/af054ac5d2c2686ff0434298ac81349b314fe1e4" width="600"></p>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="1920bbb1-9a8f-441d-92e3-5a53a07e20ca" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="6">
<li>The genie is still deciding how many days he will let the money in the purses grow. Help your friend plan a strategy for picking the purse with more money while the genie thinks.</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>Your answers may vary, but here is an example:</p>
<p>The vertical intercept for Purse B is lower, so Purse B starts off with less money than Purse A. The values in Purse B stay lower than the values in Purse A until day 10, when they appear to be the same. So Purse A is better up to day 10, and after that point Purse B becomes a better choice.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!-- "Start "Are you Ready for More? click to reveal. If you have more than one on a page, you will need to change the Data-fire/data-wait-for-events for each set.-->
<div class="os-raise-ib-cta" data-button-text="Are you ready for more?" data-fire-event="RFM1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
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</div>
<div class="os-raise-ib-cta-prompt">
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</div>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="43d22969-63af-46fc-b111-a8313be1b2f2" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<h4>Extending Your Thinking</h4>
<p>“Okay, okay,” the genie smiles, disappointed. “I will give you an even more enticing deal.” He explains that Purse B stays the same, but Purse A now increases by $250,000 every day. Which purse should you choose?</p>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Your answers may vary, but here is an example:</p>
<p>Purse B surpasses Purse A on day 30, with about $10.7 million in Purse B and only about $7.5 million in Purse A. So it’s better to choose Purse A if the amounts grow for less than 30 days, and it’s better to choose Purse B if they grow for 30 days or more.</p>
</div>
</div>
<!--End interaction-->
<br>