Question

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

Answer 1

Answer:

The average rate of change is $12$

Step-by-step explanation:

Given:

Interval; x = 3 to x = 5

We'll represent these by

x1 = 3

x2 = 5

The corresponding y values are:

When x = 3, y = 8

When x = 5, y = 32

This will also be represented

y1 = 8

y2 = 32

Average rate of change is then calculated as follows

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Where m represent average rate of change

By Substitution, we have

$m = \frac{32 - 8}{5 - 3}$

$m = \frac{24}{2}$

$m = 12$

Hence, the average rate of change is $12$

Answer 2

Answer:

B

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

$\frac{f(b)-f(a)}{b-a}$

Here [ a, b ] = [ 3, 5 ]

From the table of values

f(b) = f(5) = 32

f(a) = f(3) = 8

Hence

average rate of change = $\frac{32-8}{5-3}$ = $\frac{24}{2}$ = 12