Question

What is the average rate of change for this function for the interval from x=3 to x=5

Answer 1

The average rate of change is 12 the interval from x=3 to x=5.

How to find the average rate of change of something?

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

$\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}$

where when

$x = x_1, y = y_1\\and \\x = x_2, y = y_2$

Given:

Interval; x = 3 to x = 5

We can represent these by

$x_1 = 3\\x_2 = 5$

The corresponding y values are as follows

When x = 3, y = 8

When x = 5, y = 32

This will also be represented

$y_1 = 8\\y_2 = 32$

The average rate of change is then calculated as follows

$\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}\\\\\\m = \dfrac{32 -8}{5-3}\\\\m = \dfrac{24}{2}\\\\m = 12$

Hence, the average rate of change is 12.

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