009B Sample Midterm 1, Problem 2

Otis Taylor plots the price per share of a stock that he owns as a function of time

and finds that it can be approximated by the function

$s(t)=t(25-5t)+18$

where $t$ is the time (in years) since the stock was purchased.

Find the average price of the stock over the first five years.

Foundations:
The average value of a function $f(x)$ on an interval Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [a,b]} is given by $f_{\text{avg}}={\frac {1}{b-a}}\int _{a}^{b}f(x)~dx$.

Solution:

Step 1:
Using the formula given in Foundations, we have:
$f_{\text{avg}}=$

Step 2:

Step 3:

Final Answer:

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