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ed698135-431e-4649-a9dc-b5fe75918903.html
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<!--Do not edit this div tag. It must surround the interaction block-->
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="f224515e-e330-469d-bed0-b67356dd5cf7" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0">
<p>Complete the following questions to practice the skills you have learned in this lesson.</p>
<!--Q1-->
<div class="os-raise-ib-pset-problem" data-content-id="54e1ee56-0684-4f78-9d2e-b434955a8f28" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\( f(t)=20(\frac{1}{3})^t\)" data-solution-options='["\\( f(t)=20+ \\frac{1}{3}t\\)", "\\( f(t)=20(\\frac{1}{3})^t\\)", "\\(f(t)=20(\\frac{2}{3})^t\\)", "\\(f(t)=20+\\frac{2}{3}t\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="1" type="1">
<li>For an experiment, a scientist designs a can, 20 cm in height, that holds water. A tube is installed at the
bottom of the can allowing water to drain out.
<p>At the beginning of the experiment, the can is full. Every minute after the start of the experiment,
\(\frac23\) of the water is drained.</p>
<p>The height of the water, \(h\), in cm, is a function \(f\) of time \(t\) in minutes since the
beginning of the experiment, \(h=f(t)\). Which is an expression for \(f(t)\)?</p>
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 5.8.2–5.8.4. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(f(t)=20(\frac13)^t\).
</p>
</div>
</div>
<!--q2-->
<div class="os-raise-ib-pset-problem" data-content-id="cdc0de8f-f7ad-4b24-a42e-b6c7217de1fa" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\( b=10000 \cdot 3^d\)" data-solution-options='["\\( b=10000 \\cdot 3^d\\)", "\\(b=10000 \\cdot 3d\\)", "\\(b=10000(\\frac13)^d\\)", "\\(b=10000+3^d\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2" type="1">
<li>A bacteria population is 10,000. It triples each day.<br> The bacteria population, \(b\), is a function of
the number of days, \(d\). Which equation relates \(b\) and \(d\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 5.8.2–5.8.4 to test your understanding? Then come
back and try this question again.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \( b=10000 \cdot 3^d\).
</p>
</div>
</div>
<!--q3-->
<div class="os-raise-ib-pset-problem" data-content-id="0b3534d1-9dcd-4d60-b28a-7553f9e04c3c" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\( a=20 \cdot 1.1^t\)" data-solution-options='["\\(a=20+1.1^t\\)", "\\(a=20 \\cdot 1.1t\\)", "\\( a=20 \\cdot 1.1^t\\)", "\\(a=20-1.1^t\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3" type="1">
<li>The area, \(a\), covered by a city is 20 square miles. The area grows by a factor of 1.1 each year, \(t\),
since it was 20 square miles. Which equation expresses \(a\) in terms of \(t\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 5.8.2–5.8.4. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \( a=20 \cdot 1.1^t\).
</p>
</div>
</div>
<!--Q4-->
<div class="os-raise-ib-pset-problem" data-content-id="5778ce9d-a0fd-4fb0-ab3a-3b9bae8a95dc" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="After 2 minutes, the height of the water is \(\frac{20}{9}\) centimeters." data-solution-options='["After 2 minutes, the height of the water is \\(\\frac{20}{9}\\) centimeters less than at the start.","After \\(\\frac{20}{9}\\) minutes, the height of the water is 2 centimeters.","After 2 minutes, the height of the water is \\(\\frac{20}{9}\\) centimeters.","After \\(\\frac{20}{9}\\) minutes, the height of the water is 2 centimeters less than at the start."]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4" type="1">
<li>The graph below models the water draining out of a tube during an experiment represented by the function, \(f(t) = 20(1/3)^t\).
What does the value \((2, \frac{20}9\)) mean in the context of the problem? <br><br><img alt class="img-fluid atto_image_button_text-bottom" height="295" role="presentation" src="https://k12.openstax.org/contents/raise/resources/58c7b5ead8561c6b71a8fcb3563b7d584d51cf0b" width="300"> </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 5.8.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: After 2 minutes, the height of the water is \(\frac{20}{9}\) centimeters.
</p>
</div>
</div>
<!--Q5-->
<div class="os-raise-ib-pset-problem" data-content-id="55059bdc-fd74-48e4-855f-94fcbe04bbe3" data-problem-type="dropdown" data-retry-limit="1" data-solution="Yes" data-solution-options='["Yes", "No"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5" type="1">
<li> A scientist measures the height, \(h\), of a tree each month, and \(m\) is the number of months since the
scientist first measured the height of the tree. Is the height, \(h\), a function of the month, \(m\)?
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 5.8.3. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: Yes because the scientist measures the height of the tree each month and gets a value,
so for each value of \(m\), there will be a height \(h\). </p>
</div>
</div>
<!--Q6-->
<div class="os-raise-ib-pset-problem" data-content-id="720112a8-813a-4511-bc7c-4bf5a1f76b02" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(P=3 \cdot 2^m\)" data-solution-options='["\\( P=3+2m\\)", "\\(P=3(2m)\\)", "\\(P=3 \\cdot 2^m\\)", "\\(P=2 \\cdot 3^m\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6" type="1">
<li>Cary started with 3 goldfish in her tank, and the population doubled every month. Which is an equation that
represents the population, \(P\), of goldfish after \(m\) months?
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 5.8.2–5.8.4 to test your understanding? Then come
back and try this question again.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(P=3 \cdot 2^m\).
</p>
</div>
</div>
<!--Q#7-->
<div class="os-raise-ib-pset-problem" data-content-id="1c91e30d-674a-4571-92ed-4e12263bbee2" data-problem-comparator="integer" data-problem-type="input" data-solution="50">
<div class="os-raise-ib-pset-problem-content">
<p>Use this equation for problems 7–10:
\(f(t)=50 \cdot 2^t\)</p>
<ol class="os-raise-noindent" start="7" type="1">
<li>What is the initial value?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The initial value is 50. When
\(t=0\), \(f(t)=50 \cdot 2^0=f(t)=(50)(1)=50\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 5.8.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: The initial value is 50. When
\(t=0\),\(f(t)=50 \cdot 2^0=f(t)=(50)(1)=50\).</p>
</div>
</div>
<!--Q#8-->
<div class="os-raise-ib-pset-problem" data-content-id="e40d2def-b7bf-4139-8f97-ed505f105823" data-problem-comparator="integer" data-problem-type="input" data-solution="2">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="8" type="1">
<li>What is the growth factor?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p> Correct! The initial value is 2. The growth factor refers to the constant multiplier that determines how the
function grows or decays as the independent variable changes. In this equation, the growth factor is 2.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 5.8.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: The initial value is 2. The growth factor refers to the constant multiplier that
determines how the function grows or decays as the independent variable changes. In this equation, the growth
factor is 2.</p>
</div>
</div>
<!--Q9-->
<div class="os-raise-ib-pset-problem" data-content-id="8b18c59d-a4c8-4193-b9a3-f29c1675d9f2" data-problem-type="multiplechoice" data-retry-limit="2" data-solution="\( t\)" data-solution-options='["\\( t\\)", "\\( f(t)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="9" type="1">
<li> What is the independent variable?
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(t\), The independent variable is the variable that is manipulated or controlled and is represented by
\(t\) in this equation.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 5.8.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(t\), The independent variable is the variable that is manipulated or controlled and is
represented by \(t\) in this equation. </p>
</div>
</div>
<!--Q10-->
<div class="os-raise-ib-pset-problem" data-content-id="0e063d30-b916-44a4-b667-c051bafdbcb0" data-problem-type="multiplechoice" data-retry-limit="2" data-solution="\( f(t)\)" data-solution-options='["\\( t \\)", "\\( f(t)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="10" type="1">
<li> What is the dependent variable?
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(f(t)\), The dependent variable is the variable that depends on or is influenced by the independent variable. In this
equation, the dependent variable is \(f(t)\), which represents the output or value of the function.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 5.8.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p> \(f(t)\), The dependent variable is the variable that depends on or is influenced by the independent variable. In
this equation, the dependent variable is \(f(t)\), which represents the output or value of the function. </p>
</div>
</div>
<!--Q11-->
<div class="os-raise-ib-pset-problem" data-content-id="cb878148-c8cb-464b-9a7d-cfe8d9def838" data-problem-type="multiplechoice" data-retry-limit="2" data-solution="\(y=25 \cdot 2^x\)" data-solution-options='["\\(y=25 \\cdot (2x)^2\\)", "\\(y=25 \\cdot 2^x\\)", "\\(y=25 \\cdot x^2\\)", "\\(y=50 \\cdot 2^{\\frac 1x}\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="11">
<li>Which equation is most appropriate for modeling this data?</li>
</ol>
<table class="os-raise-horizontaltable">
<thead></thead>
<tbody>
<tr>
<th scope="row">x</th>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
</tr>
<tr>
<th scope="row">y</th>
<td>50</td>
<td>100</td>
<td>200</td>
<td>400</td>
<td>800</td>
<td>1600</td>
</tr>
</tbody>
</table>
<br>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(y=25 \cdot 2^x\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 5.8.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p> The correct answer is \(y=25 \cdot 2^x\)</p>
</div>
</div>
<!--Do not edit below this line-->
<div class="os-raise-ib-pset-correct-response"> </div>
<div class="os-raise-ib-pset-encourage-response"> </div>
</div>