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

$m=\frac{y_2-y_1}{x_2-x_1}$

for x = 1 and x = 2

$m=\frac{4-2}{2-1}=\frac{2}{1}=2$

Therefore the rate of change is 2

for x = 2 and x = 3

$m=\frac{8-4}{3-2}=\frac{4}{1}=4$

Therefore the rate of change is 4

for x = 3 and x = 4

$m=\frac{16-8}{4-3}=\frac{8}{1}=8$

Therefore the rate of change is 8