Question

What is the average rate of change of the function f(x)=5(2)^x from x = 1 to x = 5? Enter your answer in the box.

Answer 1

37.5

Explanation:

Answer 2

37.5

Explanation:

The average rate of change is the amount over an interval the outputs change in a ratio to the input change. In a linear function, this is constant and called slope. In all other function, it is called the average rate of change because the rate of change varies over the interval. We use the same formula for the average rate of change as we do slope. First we need both the inout and output values of the function over the interval.

For x=1,
`f(1)=5(2^1)=5(2)=10`.

For x=5,
`f(1)=5(2^5)=5(32)=160`

Slope:
`m=(y_2-y_1)/(x_2-x_1)`

We substitute
`x_1=1\\y_1=10` and
`x_2=5\\y_2=160`

`m=(160-10)/(5-1)`

`m=(150)/(4)=(75)/(2) =37.5`