Question

The value of the computer decreased exponentially throughout the five-year

period. What was the average annual amount of decrease in dollars per
year) over the two-year interval from t = 2 to t = 4?
(Note: Give the answer as a positive value.

Answer 1

See Explanation

Explanation:

Incomplete question as the function is not given. So, I will give a general solution

Required

Determine the average rate of change from t = 2 to 4

Average rate of change is :

`Rate = (f(b) - f(a))/(b - a)`

In this case: a = 2 and b = 4

So, we have:

`Rate = (f(4) - f(2))/(4 - 2)`

`Rate = (f(4) - f(2))/(2)`

Assume that the exponential function is:

`f(t) = 3^{-t`

f(4) and f(2) will be:

`\\ f(4) = 3^(-4) = (1)/(81)`

`f(2) = 3^(-2) = (1)/(9)`

So:

`Rate = (f(4) - f(2))/(2)`

`Rate = ((1)/(81) - (1)/(9))/(2)`

Take LCM

`Rate = ((1 - 9)/(81))/(2)`

`Rate = (-(8)/(81))/(2)`

`Rate = -(8)/(81)*(1)/(2)`

`Rate = -(4)/(81)`

So, the average rate of change is a decrease of 4/81