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261b60c4-370d-4027-a6ed-3f982dd735cc.html
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<h4>Activity</h4>
<p>Clare noticed mold on the last slice of bread in a plastic bag. The area covered by the mold was about 1 square
millimeter. She left the bread alone to see how the mold would grow. The next day, the area covered by the mold had
doubled, and it doubled again the day after that.</p>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="4db92c5b-da86-4277-93b7-7f80323187b9"
data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li> If the doubling pattern continues, how many square millimeters will the mold cover 4 days after she noticed
the mold? Be prepared to show your reasoning.</li>
</ol>
<br>
</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>16 square millimeters. \(2 \cdot 2 \cdot 2 \cdot 2\) or \(2^4\) is 16.</p>
</div>
</div>
<!--Interaction End -->
<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" start="2">
<li> Represent the relationship between the area \(A\), in square millimeters, covered by the mold and the number
of days \(d\) since the mold was spotted using:
<ol class="os-raise-noindent" type="a">
<li> A table of values, showing the values from the day the mold was spotted through 5 days later. </li>
<li> An equation </li>
<li> A graph </li>
</ol>
</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answers. 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 answers:</p>
<ol class="os-raise-noindent" type="a">
<li><br></li>
<table class="os-raise-midsizetable">
<thead>
<tr>
<th scope="col">Number of days, \(d\)</th>
<th scope="col">Area, \(A\), in sq mm</th>
</tr>
</thead>
<tbody>
<tr>
<td>
0
</td>
<td>
1
</td>
</tr>
<tr>
<td>
1
</td>
<td>
2
</td>
</tr>
<tr>
<td>
2
</td>
<td>
4
</td>
</tr>
<tr>
<td>
3
</td>
<td>
8
</td>
</tr>
<tr>
<td>
4
</td>
<td>
16
</td>
</tr>
<tr>
<td>
5
</td>
<td>
32
</td>
</tr>
</tbody>
</table>
<br>
<li> Equation: \(A=1 \cdot 2^d\) or equivalent (like \(A=2^d\)). </li>
<br>
<li>Your graph may be discrete or continuous, this example is a discrete graph.<br>
<img alt class="img-fluid atto_image_button_text-bottom" height="295" role="presentation"
src="https://k12.openstax.org/contents/raise/resources/12fcc0a764a3422882fd1d726e1ca3ad71b343f0" width="300">
</li>
</ol>
</div>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="543f6aa6-277e-4cec-ac71-691335158468"
data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li> Discuss with your partner: Is the relationship between the area covered by mold and the number of days a
function? If so, write ____ is a function of ____. If not, explain why it is not.</li>
</ol>
<br>
</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>Yes. </p>
<ul>
<li>The area covered by mold is a function of the number of days that have passed. At any given time since mold
was spotted, there is a certain area of the bread that is covered in mold.</li>
<li>The number of days that have passed is a function of the area covered by the mold up to a certain point (e.g.,
when the entire piece of bread is already completely covered, the area of mold would correspond to more than one
day). We do not have a way to write this relationship using an equation, but we could use a table or a graph to
show the relationship.</li>
</ul>
</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">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-cta-prompt">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<!--Start interaction. If multiple interactions appear under "are you ready for more?, they should all have matching "data-wait-for-event", which should also match the "data-fire-event" for the button. Note in this sample, they are all RFM1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d8cd2051-ed38-4cbd-b5f3-3ef0e09fed01"
data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<h4>Extending Your Thinking</h4>
<br>
<p>What do you think is an appropriate domain for the mold area function \(A\)? Be prepared to show your reasoning.
</p>
</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 an example.<br>Some negative values of \(t\) could be relevant, but we
don’t know how the mold was growing before Clare started watching. Positive values of \(t\) will not be
valid indefinitely as the bread will soon be completely covered by mold. If a piece of bread is 10 cm by 10 cm,
that’s 10,000 square mm. An appropriate domain would be \(0 \leq d \leq 14\).</p>
</div>
</div>
<!--End interaction-->