Question

Average Price A stock analyst plots the price per share of a certain common stock as a function of time and finds that it can be approximated by the function

S(t)=37+6e-0.03t,
where t is the time (in years) since the stock was purchased. Find the average price of the stock over the first six years.

Answer 1

42.49 unit price

Explanation:

The average price function, S(ave), will be an integral of the price function over the period of time (6 years), that is

S(ave) =
`1/6*\int\limits^6_0 {S(t)} \, dt`

=
`1/6*\int\limits^6_0 {37+6e^-0.03t} \, dt`

Solving the integral, we have

S(ave) = 1/6*(37t - (6e^-0.03t)/0.03) with the limits being from t = 0 to t = 6

Hence, we have

S(ave) =
`37 - (200)/(6)*(e^(-0.03*6) - 1)`

This resolves to 42.49 unit price