Question

What is the average rate of change betweenx = 1 and x = 2?x = 2 and x = 3?x = 3 and x = 4?

Answer 1

We have the following:

The rate of change is the same as the slope.

The slope can be calculated as follows

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

for x = 1 and x = 2

`m=(4-2)/(2-1)=(2)/(1)=2`

Therefore the rate of change is 2

for x = 2 and x = 3

`m=(8-4)/(3-2)=(4)/(1)=4`

Therefore the rate of change is 4

for x = 3 and x = 4

`m=(16-8)/(4-3)=(8)/(1)=8`

Therefore the rate of change is 8