Answer:
The rate of change is -1.5.
Step-by-step explanation:
Given : Function [tex]g(x)=\frac{3}{2}x+1[/tex]
To find : The average rate of change of the function over the interval -2<x<8?
Solution :
The average rate of function f(x) between the interval a and b is given by,
[tex]\text{Rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]
Here, [tex]g(x)=\frac{3}{2}x+1[/tex] and a=-2 and b=8
[tex]\text{Rate of change}=\frac{g(-2)-g(8)}{8-(-2)}[/tex]
[tex]g(-2)=\frac{3}{2}(-2)+1[/tex]
[tex]g(-2)=-3+1[/tex]
[tex]g(-2)=-2[/tex]
[tex]g(8)=\frac{3}{2}(8)+1[/tex]
[tex]g(8)=12+1[/tex]
[tex]g(8)=13[/tex]
Substitute,
[tex]\text{Rate of change}=\frac{-2-(13)}{8-(-2)}[/tex]
[tex]\text{Rate of change}=\frac{-15}{10}[/tex]
[tex]\text{Rate of change}=-1.5[/tex]
Therefore, the rate of change is -1.5.
