Question

For the graphed function f(x) = (4)x - 1 + 2, calculate the average rate of change from x = 2 to x = 4.

Answer 1

`Average = 30`

Explanation:

Given

`f(x) = 4^(x - 1) + 2`

Required

Average
`rate\ of\ change` from 2 to 4

This is calculated using:

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

Where

`a= 2` and
`b = 4`

So:

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

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

Calculate f(2) and f(4)

`f(x) = 4^(x - 1) + 2`

`f(2) = 4^(2-1) + 2`

`f(2) = 4 + 2`

`f(2) = 6`

`f(4) = 4^(4-1) + 2`

`f(4) = 4^3 + 2`

`f(4) = 66`

So:

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

`Average = (66 - 6)/(2)`

`Average = (60)/(2)`

`Average = 30`