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Similar Question 1
<p>For each of the following functions, calculate the average rate of change on the interval <code class='latex inline'>x \epsilon [2,5]</code>.</p><p><code class='latex inline'>g(x)=\displaystyle{\frac{1}{x}}</code></p>
Similar Question 2
<p>Determine the average rate of change from <code class='latex inline'>x=1</code> to <code class='latex inline'>x=4</code> the each function.</p><p> <code class='latex inline'> \displaystyle y = x </code></p>
Similar Question 3
<p>For each of the following functions, calculate the average rate of change on the interval <code class='latex inline'>x \epsilon [2,5]</code>.</p><p><code class='latex inline'>g(x)=\displaystyle{\frac{1}{x}}</code></p>
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Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Estimate the average rate of change from <code class='latex inline'>x = -3</code> to <code class='latex inline'>x = 2</code> for each function.</p><p><code class='latex inline'>\displaystyle y =2x - 1</code></p>
<p>What is the average rate of change for the function <code class='latex inline'>g(x) =4x^2 - 5x + 1</code> over the interval below?</p><p><code class='latex inline'>2 \leq x \leq 2.1</code></p>
<p>For each of the following functions, calculate the average rate of change on the interval <code class='latex inline'>x \in [2,5]</code>.</p><p><code class='latex inline'>t(x)=3x^2-4x+1</code></p>
<p>The purchase price, <code class='latex inline'>P</code>, of one share in company at any time, <code class='latex inline'>t</code>, in years, can be modelled by the function <code class='latex inline'>P(t) = -0.2t^3 + 2t^2 + 8t + 2, t\in[0, 13]</code>.</p><p> Graph the function by using a graphing device.</p><p> Use the graph to describe when the rate of change is positive, when it is zero, and when it is negative.</p>
<p>The population of a town is modelled by <code class='latex inline'>P(t) = 50t^2 + 1000t + 20 000</code> is the size of the population and t is the number of years since 2000.</p><p> Predict if the average rate of change in the population size will be greater closer to the year 2000 or farther in the future. Explain how you made your prediction.</p><p>Show your work.</p>
<p>Estimate the average rate of change from <code class='latex inline'>x = -3</code> to <code class='latex inline'>x = 2</code> for each function.</p><p><code class='latex inline'>\displaystyle y =x^2 +3x</code></p>
<p>Determine the average rate of change from <code class='latex inline'>x=1</code> to <code class='latex inline'>x=4</code> the each function.</p><p> <code class='latex inline'> \displaystyle y = x </code></p>
<p>What is the average rate of change in the values of the function <code class='latex inline'>f(x)= 4x</code> from <code class='latex inline'>x = 2 </code> to <code class='latex inline'>x =6</code>? </p><p>What about from <code class='latex inline'>x =2</code> to <code class='latex inline'>x=26</code>?</p>
<p>For each of the following functions, calculate the average rate of change on the interval <code class='latex inline'>x \in [2,5]</code>.</p><p><code class='latex inline'>v(x)=9</code></p>
<p>What is the average rate of change for the function <code class='latex inline'>g(x) =4x^2 - 5x + 1</code> over the interval below?</p><p><code class='latex inline'>2 \leq x \leq 3</code></p>
<p>For each of the following functions, calculate the average rate of change on the interval <code class='latex inline'>x \epsilon [2,5]</code>.</p><p><code class='latex inline'>g(x)=\displaystyle{\frac{1}{x}}</code></p>
<p>What is the average rate of change for the function <code class='latex inline'>g(x) =4x^2 - 5x + 1</code> over the interval below?</p><p><code class='latex inline'>2 \leq x \leq 2.25</code></p>
<p>What is the average rate of change for the function <code class='latex inline'>g(x) =4x^2 - 5x + 1</code> over the interval below?</p><p><code class='latex inline'>2 \leq x \leq 4</code></p>
<p>During the Apollo 14 mission, Alan Shepard hit a golf ball on the Moon. The function <code class='latex inline'>h(t) =18t-0.8t^2</code> models the height of the golf ball’s trajectory on the Moon, where <code class='latex inline'>h(t)</code> is the height, in metres, of the ball above the surface of the Moon and <code class='latex inline'>t</code> is the time in seconds. What is the average rate of change in the height of the ball over the time interval <code class='latex inline'>10 \leq t \leq 15</code>? Show your work.</p>
<p>For each of the following functions, calculate the average rate of change on the interval <code class='latex inline'>x \in [2,5]</code>.</p><p><code class='latex inline'>h(x)=2^x</code></p>
<p>Consider the function <code class='latex inline'>f(x)=3(x-2)^2-2</code>.</p><p>Determine the average rate of change in on each of the following intervals.</p><p>i) <code class='latex inline'>2 \leq x \leq 4</code></p><p>ii) <code class='latex inline'>2 \leq x \leq 6</code></p><p>iii) <code class='latex inline'>4 \leq x \leq 6</code></p>
<p>What is the average rate of change for the function <code class='latex inline'>g(x) =4x^2 - 5x + 1</code> over the interval below?</p><p><code class='latex inline'>2 \leq x \leq 3</code></p>
<p>Determine the average rate of change from <code class='latex inline'>x=1</code> to <code class='latex inline'>x=4</code> the each function.</p><p><code class='latex inline'> \displaystyle y = 7 </code></p>
<p>What is the average rate of change for the function <code class='latex inline'>g(x) =4x^2 - 5x + 1</code> over the interval below?</p><p><code class='latex inline'>2 \leq x \leq 2.01</code></p>
<p>For each of the following functions, calculate the average rate of change on the interval <code class='latex inline'>x \in [2,5]</code>.</p><p><code class='latex inline'>f(x)=3x+1</code></p>
<p>A company that sells sweatshirts finds that the profit can be modelled by </p><p><code class='latex inline'>P(s)= -0.30s^2 + 3.5s + 11.5</code>, where P(s) is the profit, in thousands of dollars, and s is the number of sweatshirts sold (expressed in thousands).</p><p><strong>(a)</strong> What is the average rate of change in profit for the following intervals?</p> <ul> <li><code class='latex inline'>1\leq s \leq 2 </code></li> <li><code class='latex inline'>2 \leq s \leq 3</code></li> <li><code class='latex inline'>3 \leq s \leq 4</code></li> <li><code class='latex inline'>4\leq s \leq 5</code></li> </ul> <p><strong>(b)</strong> As the number of sweatshirts sold increases, what do you notice about the average rate of change in profit on each sweatshirt? </p><p><strong>(c)</strong> At what point does rate of change in profit turn negative?</p><p>Show your work.</p>
<p>Determine the average rate of change from <code class='latex inline'>x=1</code> to <code class='latex inline'>x=4</code> the each function.</p><p><code class='latex inline'> \displaystyle y = x^2 </code></p>
<p>The population of a town is modelled by <code class='latex inline'>P(t) = 50t^2 + 1000t + 20 000</code> is the size of the population and t is the number of years since <code class='latex inline'>2000</code>.</p><p>What is the average rate of change in the population size for each</p> <ul> <li>i) <code class='latex inline'>2000 - 2010</code></li> <li>ii) <code class='latex inline'>2005-2015</code></li> <li>iii) <code class='latex inline'>2002-2012</code></li> <li>iv) <code class='latex inline'>2010-2020</code></li> </ul>
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