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mattboelkins merged 1 commit into from
Jun 25, 2025
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Jen's questions for proteus-1-1 #376

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128 changes: 128 additions & 0 deletions source/proteus/proteus-1-1.xml
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<?xml version="1.0" encoding="UTF-8" ?>
<!-- **********************************************************************-->
<!-- Copyright 2012-2026 -->
<!-- Matthew Boelkins -->
<!-- -->
<!-- This file is part of Active Calculus. -->
<!-- -->
<!-- Permission is granted to copy, distribute and/or modify this document -->
<!-- under the terms of the Creative Commons BY-SA license. The work -->
<!-- may be used for free by any party so long as attribution is given to -->
<!-- the author(s), the work and its derivatives are used in the spirit of -->
<!-- "share and share alike". All trademarks are the registered marks of -->
<!-- their respective owners. -->
<!-- **********************************************************************-->
<exercises component="proteus" xmlns:xi="http://www.w3.org/2001/XInclude" xml:id="proteus-1-1">
<title>PROTEUS exercises</title>
<p>
In part <xref ref="PA-1-1" text="type-global"/>, you explored the velocity of a ball at various times. Answer the following questions to explore other rates of change.
</p>
<exercise component="proteus" label="proteus-rates-o-change" xml:id="proteus-rates-o-change" attachment="yes">
<p>
For each of the following scenarios, specify the independent (input) and dependent (output) variables, along with possible units for both. Then give units for the rate of change.
</p>
<ol>
<li>
<p>
The population of a city changes over time.
<ol>
<li>
<p>
Independent: <response />
</p>
</li>
<li>
<p>
Dependent: <response />
</p>
</li>
<li>
<p>
Rate of change: <response />
</p>
</li>
</ol>
</p>
</li>
<li>
<p>
As a weather balloon rises, the temperature of the air inside (and outside) the balloon decreases.
<ol>
<li>
<p>
Independent: <response />
</p>
</li>
<li>
<p>
Dependent: <response />
</p>
</li>
<li>
<p>
Rate of change: <response />
</p>
</li>
</ol>
</p>

</li>
<li>
<p>
For a given trip (i.e. a set distance) as the speed of the car increases, the travel time decreases.
<ol>
<li>
<p>
Independent: <response />
</p>
</li>
<li>
<p>
Dependent: <response />
</p>
</li>
<li>
<p>
Rate of change: <response />
</p>
</li>
</ol>
</p>

</li>
<li>
<p>
As the population of a city decreases, the tax revenue of the city also decreases.
<ol>
<li>
<p>
Independent: <response />
</p>
</li>
<li>
<p>
Dependent: <response />
</p>
</li>
<li>
<p>
Rate of change: <response />
</p>
</li>
</ol>
</p>
</li>
</ol>

</exercise>


<exercise component="proteus" label="proteus-example-roc" xml:id="proteus-example-roc" attachment="yes">

<p>
Give your own example of a quantity that changes over time, the units of the independent and dependent variables, and units of the rate of change.
</p>
<response />

</exercise>
</exercises>
4 changes: 3 additions & 1 deletion source/sec-1-1-vel.xml
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</p>

<xi:include href="./previews/PA-1-1-WW.xml" />
<xi:include href="./previews/PA-1-1.xml" />
<xi:include href="./previews/PA-1-1.xml" />
</introduction>

<xi:include href="./proteus/proteus-1-1.xml" />

<subsection permid="iwq">
<title>Position and average velocity</title>
<p permid="Pnt">
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