Question

Average Price 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.

Answer 1

Answer: The average price is $72.166.

Step-by-step explanation:

Since we have given that

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

We need to find the average price of the stock over the first five years.

So, Average price would be

$\dfrac{1}{b-a}\int\limits^a_b {t(25-5t)+18} \, dt\\\\ =\dfrac{1}{5}\int\limits^5_0 {25t-5t^2+18} \, dt\\\\ =\dfrac{1}{5}{\dfrac{25t^2}{2}-\dfrac{5t^3}{3}+18t|^5_0 \\\\=\dfrac{1}{5}[\dfrac{25\times 25}{2}-\dfrac{125}{3}+18\times 5]\\\\=\dfrac{1}{5}[312.5-41.67+90]\\\\=72.166$

Hence, the average price is $72.166.