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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.

User Samet
by
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1 Answer

13 votes

Answer:

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

User Gameplay
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