Answer :
Average rate of the function: 3
Step-by-step explanation:
The function in this problem is
[tex]f(x)=4^{x-1}+2[/tex]
The average rate of change of a function over an interval [tex](x_1,x_2)[/tex] is given by
[tex]r=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
where
[tex]f(x_1),f(x_2)[/tex] are the values of the function calculated in [tex]x_1,x_2[/tex] respectively
For the function in this problem we have:
[tex]x_1=1[/tex], so
[tex]f(x_1)=f(1)=4^{1-1}+2=4^0+2=1+2=3[/tex]
[tex]x_2=2[/tex], so
[tex]f(x_2)=f(2)=4^{2-1}+2=4^1+2=4+2=6[/tex]
So, the average rate of change is
[tex]r=\frac{6-3}{2-1}=\frac{3}{1}=3[/tex]
Learn more about rate of change:
brainly.com/question/4152194
brainly.com/question/12941985
#LearnwithBrainly