Now You Try

<p>An emergency flare is shot into the air. Its height, in metres, above the ground at various times in its flight is given in the following table.</p><img src="/qimages/162" /><p>Is the height increasing or decreasing at the given intervals below?</p>
<ul>
<li><code class='latex inline'>1.0 \leq t \leq 2.0 </code></li>
<li><code class='latex inline'>3.0 \leq t \leq 4.0 </code></li>
</ul>
<p>Show your work.</p>

<p>This table shows the growth of a crowd at a rally over a 3 period.</p><img src="/qimages/163" /><p> What is the average rate of change in the size of the crowd for each half hour of the rally?</p><p>Show your work.</p>

<p>Rachel climbed Mt. Fuji while in Japan. There are 10 levels to the mountain. She was able to drive to Level 5, where she began her climb.</p>
<ul>
<li>She walked at a constant rate for 40 min from Level 5 to Level 6.</li>
<li>She slowed slightly but then continued at a constant rate for a total
of 90 min from Level 6 to Level 7.</li>
<li>She decided to eat and rest there, which took approximately 2 h.</li>
<li>From Level 7 to Level 8, a 40 min trip, she travelled at a constant rate.</li>
<li>Continuing on to Level 9, a 45 min trip, she decreased slightly to
a new constant rate.</li>
<li>During most of the 1 h she took to reach Level 10, the top of
Mt. Fuji, she maintained a constant rate. As she neared the top,
however, she accelerated.</li>
</ul>
<img src="/qimages/122" /><p>What is Rachel's average speed over each part of her climb?</p>

<p>The cumulative distance traveled over several days of the 2007 Tour de France bicycle race is shown in the table at the bottom. What is the average rate of change in cumulative distance traveled between consecutive days? Show your work.</p><img src="/qimages/115" />

<p>It is estimated that, <code class='latex inline'>t</code> years from now, that amount of waste accumulated <code class='latex inline'>Q</code>, in tonnes, will be <code class='latex inline'>Q(t)=10^4(t^2+15t+70), 0\leq t \leq 10</code>.</p><p>What will be the average rate of change in this quantity over the next three years?</p>

<p>Does the Tour de France race travel over the same distance each day? Explain.</p><img src="/qimages/115" />

<p>The table shows the percent of Canadian households that used e-mail from 1999 to 2003.</p><img src="/qimages/130" /><p>Determine the average rate of change of the percent of households using e-mail from 1999 to 2003. What are the units for this average rate of change?</p>

<p>The following table shows the daily number of watches sold at a shop and the amount of money made from the sales.</p><img src="/qimages/1691" /><p><strong>a)</strong> Does the data in the table appear to follow a linear relation? Explain.</p><p><strong>b)</strong> What is the average rate of change in revenue from <code class='latex inline'>w = 20</code> to <code class='latex inline'>w = 25</code>?</p><p><strong>c)</strong> What is the cost of one watch, and how does this cost relate to the graph?</p>

<p>An emergency flare is shot into the air. Its height, in metres, above the ground at various times in its flight is given in the following table.</p><img src="/qimages/162" /><p>What is the average rate of change in the height of the flare during each interval?</p><p>i) <code class='latex inline'>1.0 \leq t \leq 2.0 </code>
ii) <code class='latex inline'>3.0 \leq t \leq 4.0 </code></p><p>Show your work.</p>

<p>After <code class='latex inline'>t</code> minutes of growth, a certain bacterial culture has a mass, in grams, of <code class='latex inline'>M(t)=t^2</code>.</p><p>How much does the bacterial culture grow during the time <code class='latex inline'>3\leq t \leq 3.01</code>?</p>

<p>After <code class='latex inline'>t</code> minutes of growth, a certain bacterial culture has a mass, in grams, of <code class='latex inline'>M(t)=t^2</code>.</p><p>What is its average rate of growth during the time interval <code class='latex inline'>3\leq t \leq 3.01</code>?</p>

<p>The population of a city has continued to grow since 1950. The population <code class='latex inline'>P</code>, in thousands, and the time <code class='latex inline'>t</code>, in years, since 1950 are given in the table below and in the graph.</p><img src="/qimages/118" /><img src="/qimages/117" />
<ul>
<li>What is the average rate of change in population for the following intervals of time?</li>
</ul>
<p>Show your work.</p>