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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
+
16
e
−
0.04
t
, where t
is the time (in years) since the stock was purchased. Find the average price of the stock over the first eight years.

Answer :

The average price of the stock over the first eight years is 50.69 units / year .

Given :

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 + 16 e^0.04t.

We find the average value of the stock ,

[tex]f_{ave} =1/b-a \int\limits^8_0 {f(x)} \, dx[/tex]

[tex]f_{ave} =1/8-0 \int\limits^8_0 {S (t)} \, dx[/tex]

[tex]f_{ave} =1/8( \int\limits^8_0 {37} \, dt + \int\limits^8_0 {16e^{(0.04t) \, dt[/tex]

= 37 / 8 ( 8 - 0 ) - 1 / 0.02 ( [tex]e^{-0.04 * 8 }[/tex] - [tex]e^{-0.04 * 0[/tex])

= 50.69 units / year.

Learn more about the average here:

https://brainly.com/question/29306232

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