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<!--Do not edit this div tag. It must surround the interaction block-->
<p>Complete the following questions to practice the skills you have learned in this lesson.</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="5bb17a36-1426-4442-9b45-29f3657075e2" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0">
<!--1a-->
<div class="os-raise-ib-pset-problem" data-content-id="4b80f75e-83fa-47fa-908b-5f41956b3084" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="Grows by increasing amounts but by decreasing growth factors." data-solution-options='["Grows by increasing amounts but by decreasing growth factors.", "Changes exponentially. It doubles.", "Grows by decreasing amounts but by increasing growth factors.", "Changes logarithmically. It has decreased by one-half."]'>
<div class="os-raise-ib-pset-problem-content">
<p>Use the following to answer questions 1–7.</p>
<p>The table shows values of the expressions \(10x^2\) and \(2^x\).</p>
<table class="os-raise-skinnytable">
<thead>
<tr>
<th scope="col">\(x\)</th>
<th scope="col">\(10x^2\)</th>
<th scope="col">\(2^x\)</th>
</tr>
</thead>
<tbody>
<tr>
<td>\(1\)</td>
<td>\(10\)</td>
<td>\(2\)</td>
</tr>
<tr>
<td>\(2\)</td>
<td>\(40\)</td>
<td>\(4\)</td>
</tr>
<tr>
<td>\(3\)</td>
<td>\(90\)</td>
<td>\(8\)</td>
</tr>
<tr>
<td>\(4\)</td>
<td>\(160\)</td>
<td>\(16\)</td>
</tr>
<tr>
<td>\(8\)</td>
<td> </td>
<td> </td>
</tr>
<tr>
<td>\(10\)</td>
<td> </td>
<td> </td>
</tr>
<tr>
<td>\(12\)</td>
<td> </td>
<td> </td>
</tr>
</tbody>
</table>
<br>
<ol class="os-raise-noindent">
<li>Complete the statement.</li>
<br>
<ol class="os-raise-noindent" type="a">
<li> When the value of \(x\) increases by \(1\), the expression \(10x^2\):</li>
</ol>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! When the value of \(x\) increases by \(1\), the expression \(10x^2\) grows by increasing amounts but
by decreasing growth factors.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.4.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: When the value of \(x\) increases by \(1\), the expression \(10x^2\) grows by increasing
amounts but by decreasing growth factors.
</p>
</div>
</div>
<!--1b-->
<div class="os-raise-ib-pset-problem" data-content-id="8faaff31-6900-41de-8a2d-b80d6410eef6" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="Changes exponentially. It doubles." data-solution-options='["Grows by increasing amounts but by decreasing growth factors.", "Changes exponentially. It doubles.", "Grows by decreasing amounts but by increasing growth factors.", "Changes logarithmically. It has decreased by one-half."]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2" type="a">
<li> When the value of \(x\) increases by \(1\), the expression \(2^x\):</li>
</ol>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! When the value of \(x\) increases by \(1\), the expression \(2^x\) changes exponentially. It doubles.
</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.4.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: When the value of \(x\) increases by \(1\), the expression \(2^x\) changes
exponentially. It doubles.
</p>
</div>
</div>
<!--2-->
<div class="os-raise-ib-pset-problem" data-content-id="8e5a4f31-c589-4967-9720-c254217f286b" data-problem-type="dropdown" data-retry-limit="1" data-solution="greater than" data-solution-options='["greater than", "less than"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<li>Will the value of \(10x^2\) be greater than or less than \(2^x\) when \(x\) is \(8\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The value of \(10x^2\) will be greater than \(2^x\) when \(x\) is \(8\).
</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.4.2 and 7.4.3. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: The value of \(10x^2\) will be greater than \(2^x\) when \(x\) is \(8\).
</p>
</div>
</div>
<!--3-->
<div class="os-raise-ib-pset-problem" data-content-id="5f718188-4505-4e71-963d-58f11b82edeb" data-problem-type="dropdown" data-retry-limit="1" data-solution="greater than" data-solution-options='["greater than", "less than"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3">
<li>Will the value of \(2^x\) be greater than or less than \(10x^2\) when \(x\) is \(10\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The value of \(2^x\) will be greater than \(10x^2\) when \(x\) is \(10\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.4.2 and 7.4.3. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: The value of \(2^x\) will be greater than \(10x^2\) when \(x\) is \(10\). </p>
</div>
</div>
<!--q4-->
<div class="os-raise-ib-pset-problem" data-content-id="f994a359-6d8c-4c0e-a52a-1881e76fddee" data-problem-type="dropdown" data-retry-limit="1" data-solution="less than" data-solution-options='["greater than", "less than"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li>Will the value of \(10x^2\) be greater than or less than \(2^x\) when \(x\) is \(12\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The value of \(10x^2\) will be less than \(2^x\) when \(x\) is \(12\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.4.2 and 7.4.3. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: The value of \(10x^2\) will be less than \(2^x\) when \(x\) is \(12\).
</p>
</div>
</div>
<!--5a-->
<div class="os-raise-ib-pset-problem" data-content-id="d5b7d872-1b85-4b80-b66c-70b4f87e9d07" data-problem-comparator="integer" data-problem-type="input" data-solution="640">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li>Determine the following values of \(10x^2\).</li>
<br>
<ol class="os-raise-noindent" type="a">
<li> What is the value of \(10x^2\) when \(x\) is \(8\)?</li>
</ol>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! When \(x=8\), the value of \(10x^2\) is \(640\). </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.4.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: When \(x=8\), the value of \(10x^2\) is \(640\). </p>
</div>
</div>
<!--5b-->
<div class="os-raise-ib-pset-problem" data-content-id="705515a5-0d88-4824-b33d-09be5291b64f" data-problem-comparator="integer" data-problem-type="input" data-solution="1000">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2" type="a">
<li> What is the value of \(10x^2\) when \(x\) is \(10\)? </li>
</ol>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! When \(x=10\), the value of \(10x^2\) is \(1000\). </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.4.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: When \(x=10\), the value of \(10x^2\) is \(1000\). </p>
</div>
</div>
<!--5c-->
<div class="os-raise-ib-pset-problem" data-content-id="a4152af5-599e-42fa-9475-7c5b64709d38" data-problem-comparator="integer" data-problem-type="input" data-solution="1440">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="3" type="a">
<li> What is the value of \(10x^2\) when \(x\) is \(12\)?</li>
</ol>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! When \(x=12\), the value of \(10x^2\) is \(1440\). </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.4.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: When \(x=12\), the value of \(10x^2\) is \(1440\). </p>
</div>
</div>
<!--6a-->
<div class="os-raise-ib-pset-problem" data-content-id="37027873-e96f-4d70-8e77-f20e2bbd7858" data-problem-comparator="integer" data-problem-type="input" data-solution="256">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6">
<li>Determine the following values of \(2^x\).
</li>
<br>
<ol class="os-raise-noindent" type="a">
<li> What is the value of \(2^x\) when \(x\) is \(8\)? </li>
</ol>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! When \(x=8\), the value of \(2^x\) is \(256\). </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.4.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: When \(x=8\), the value of \(2^x\) is \(256\). </p>
</div>
</div>
<!--6b-->
<div class="os-raise-ib-pset-problem" data-content-id="d5128dc7-5a90-47d9-833d-59629ceb89e7" data-problem-comparator="integer" data-problem-type="input" data-solution="1024">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2" type="a">
<li> What is the value of \(2^x\) when \(x\) is \(10\)? </li>
</ol>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! When \(x=10\), the value of \(2^x\) is \(1024\). </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.4.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: When \(x=10\), the value of \(2^x\) is \(1024\). </p>
</div>
</div>
<!--6c-->
<div class="os-raise-ib-pset-problem" data-content-id="7cea577a-7c41-4637-bb49-e502c9900882" data-problem-comparator="integer" data-problem-type="input" data-solution="4096">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="3" type="a">
<li> What is the value of \(2^x\) when \(x\) is \(12\)?</li>
</ol>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! When \(x=12\), the value of \(2^x\) is \(4096\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.4.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: When \(x=12\), the value of \(2^x\) is \(4096\). </p>
</div>
</div>
<!--q7-->
<div class="os-raise-ib-pset-problem" data-content-id="5f1f6d4a-2063-423d-b50d-ef721491cfdc" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="The value of the exponential expression grows much more quickly as \(x\) increases." data-solution-options='["The value of the exponential expression grows much more quickly as \\(x\\) increases.", "The value of the quadratic expression grows much more quickly as \\(x\\) increases.", "They both grow at the same rate.", "There is no change in the values of the expressions when \\(x\\) increases."]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7">
<li>Choose the best statement that describes how the values of the exponential expression \(2^x\) and the
quadratic expression \(10x^2\) change as \(x\) becomes greater and greater.</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The value of the exponential expression grows much more quickly as \(x\) increases.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.4.2 and 7.4.3. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: The value of the exponential expression grows much more quickly as \(x\) increases. </p>
</div>
</div>
<!--8a-->
<div class="os-raise-ib-pset-problem" data-content-id="1ade4671-a4e8-4dfc-8bd1-b829a50b4e25" data-problem-type="dropdown" data-retry-limit="2" data-solution="exponential" data-solution-options='["exponential", "quadratic", "linear"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="8">
<li>Answer the following questions about functions \(f(x)\) and \(g(x)\).</li>
<br>
<ol class="os-raise-noindent" type="a">
<li> What type of expression is \(f(x)=1.5^x\)? </li>
</ol>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(f(x)=1.5^x\) is an exponential expression.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.4.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \(f(x)=1.5^x\) is an exponential expression. </p>
</div>
</div>
<!--8b-->
<div class="os-raise-ib-pset-problem" data-content-id="7e9ff011-14bb-48df-a9e1-c15379946ea4" data-problem-type="dropdown" data-retry-limit="2" data-solution="quadratic" data-solution-options='["exponential", "quadratic", "linear"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2" type="a">
<li> What type of expression is \(g(x)=500x^2+345x\)? </li>
</ol>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(g(x)=500x^2+345x\) is a quadratic expression.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.4.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \(g(x)=500x^2+345x\) is a quadratic expression. </p>
</div>
</div>
<!--8c-->
<div class="os-raise-ib-pset-problem" data-content-id="3161a9b3-dd78-407a-ba76-a63b3e7e778e" data-problem-type="multiplechoice" data-retry-limit="1" data-solution="Function \(f(x)\)" data-solution-options='["Function \\(f(x)\\)", "Function \\(g(x)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="3" type="a">
<li> The values of which function will eventually be greater for larger and larger values of \(x\)? </li>
</ol>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The exponential function, \(f\), will eventually be greater for larger and larger values of \(x\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.4.2 and 7.4.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: The exponential function, \(f\), will eventually be greater for larger and larger values
of \(x\). </p>
</div>
</div>
<!--9-->
<div class="os-raise-ib-pset-problem" data-content-id="f710b5e0-1775-4c25-8da8-e04c35ea4aff" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="The value of \(100x^2\) grows by different factors and the value of \(4^x\) grows by a factor of 4 every time." data-solution-options='["The value of \\(100x^2\\) grows by different factors and the value of \\(4^x\\) grows by a factor of 4 every time.", "The value of \\(100x^2\\) grows by a factor of 4 every time and the value of \\(4^x\\) grows by different factors.", "The value of \\(100x^2\\) grows by different factors and the value of \\(4^x\\) grows by a factor of \\(x\\) every time.", "The value of \\(100x^2\\) grows by a factor of \\(x\\) every time and the value of \\(4^x\\) grows by different factors."]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="9">
<li>The table shows the values of \(4^x\) and \(100x^2\) for some values of \(x\).
<br>
<table class="os-raise-skinnytable">
<thead>
<tr>
<th scope="col">\(x\)</th>
<th scope="col">\(4^x\)</th>
<th scope="col">\(100x^2\)</th>
</tr>
</thead>
<tbody>
<tr>
<td>\(1\)</td>
<td>\(4\)</td>
<td>\(100\)</td>
</tr>
<tr>
<td>\(2\)</td>
<td>\(16\)</td>
<td>\(400\)</td>
</tr>
<tr>
<td>\(3\)</td>
<td>\(64\)</td>
<td>\(900\)</td>
</tr>
<tr>
<td>\(4\)</td>
<td>\(256\)</td>
<td>\(1,600\)</td>
</tr>
<tr>
<td>\(5\)</td>
<td>\(1,024\)</td>
<td>\(2,500\)</td>
</tr>
</tbody>
</table>
<br>
<p>Looking at the patterns in the table, choose the best answer to explain why, as the value of \(x\)
increases, the values of the exponential expression \(4^x\) will eventually overtake the values of the
quadratic expression \(100x^2\).</p>
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The value of \(100x^2\) grows by different factors, and the value of \(4^x\) grows by a factor of 4
every time.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.4.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: The value of \(100x^2\) grows by different factors, and the value of \(4^x\) grows by a
factor of 4 every time.
</p>
</div>
</div>
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<div class="os-raise-ib-pset-correct-response"> </div>
<div class="os-raise-ib-pset-encourage-response"> </div>
</div>