Question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 5\le x \le 75≤x≤7.

Answer 1

Answer:

$Average\ Rate = 48$

Step-by-step explanation:

Given

See attachment for table

Required

Determine the average rate of change over $5\le x \le 7$

Average rate of change is calculated using:

$Average\ Rate = \frac{f(b) - f(a)}{b - a}$

Where

$a \le x\le b$

In this case:

$a = 5;\ \ \ b = 7$

$Average\ Rate = \frac{f(b) - f(a)}{b - a}$

$Average\ Rate = \frac{f(7) - f(5)}{7 - 5}$

$Average\ Rate = \frac{f(7) - f(5)}{2}$

From the table:

$f(7) = 108$

$f(5) = 12$

The expression becomes

$Average\ Rate = \frac{108 - 12}{2}$

$Average\ Rate = \frac{96}{2}$

$Average\ Rate = 48$