Question

What is the average rate of change of the function `f(x)=2(3)^x` from x=2 to x=4?

Answer 1

Use the slope formula to find the average rate of change:
`m=frac{y_2-y_1}{x_2-x_1}`

`m=frac{f(4)-f(2)}{4-2}`

To simplify this, we need to find values of `f(4)` and `f(2)`:
`f(4)=2(3)^4 = 2(81)=162`
`f(2)=2(3)^2=2(9)=18`

`m=frac{162-18}{2}`

`m=144/2`

`m=72`