Answer:
[tex]Average\ Rate = 48[/tex]
Step-by-step explanation:
Given
See attachment for table
Required
Determine the average rate of change over [tex]5\le x \le 7[/tex]
Average rate of change is calculated using:
[tex]Average\ Rate = \frac{f(b) - f(a)}{b - a}[/tex]
Where
[tex]a \le x\le b[/tex]
In this case:
[tex]a = 5;\ \ \ b = 7[/tex]
[tex]Average\ Rate = \frac{f(b) - f(a)}{b - a}[/tex]
[tex]Average\ Rate = \frac{f(7) - f(5)}{7 - 5}[/tex]
[tex]Average\ Rate = \frac{f(7) - f(5)}{2}[/tex]
From the table:
[tex]f(7) = 108[/tex]
[tex]f(5) = 12[/tex]
The expression becomes
[tex]Average\ Rate = \frac{108 - 12}{2}[/tex]
[tex]Average\ Rate = \frac{96}{2}[/tex]
[tex]Average\ Rate = 48[/tex]
