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.

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

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

Hence, the average price is $72.166.