contestada

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.

Respuesta :

MrRoyal

Answer:

See Explanation

Step-by-step 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 :

[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]

In this case: a = 2 and b = 4

So, we have:

[tex]Rate = \frac{f(4) - f(2)}{4 - 2}[/tex]

[tex]Rate = \frac{f(4) - f(2)}{2}[/tex]

Assume that the exponential function is:

[tex]f(t) = 3^{-t[/tex]

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

[tex]\\ f(4) = 3^{-4} = \frac{1}{81}[/tex]

[tex]f(2) = 3^{-2} = \frac{1}{9}[/tex]

So:

[tex]Rate = \frac{f(4) - f(2)}{2}[/tex]

[tex]Rate = \frac{\frac{1}{81} - \frac{1}{9}}{2}[/tex]

Take LCM

[tex]Rate = \frac{\frac{1 - 9}{81}}{2}[/tex]

[tex]Rate = \frac{-\frac{8}{81}}{2}[/tex]

[tex]Rate = -\frac{8}{81}*\frac{1}{2}[/tex]

[tex]Rate = -\frac{4}{81}[/tex]

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