Average rate of change of the function [tex]=\frac{75}{2}[/tex]
Solution:
Given function: [tex]f(x)=5(2)^{x}[/tex] from x = 1 to x = 5
Substitute x = 1 and x = 5 in f(x).
[tex]f(1)=5(2)^{1}=10[/tex]
[tex]f(5)=5(2)^{5}=160[/tex]
Let us find the average rate of change of the function.
Average rate of change
[tex]$=\frac{f(b)-f(a)}{b-a}[/tex]
Here a = 1 and b = 5.
[tex]$=\frac{f(5)-f(1)}{5-1}[/tex]
Substitute f(5) and f(1).
[tex]$=\frac{160-10}{4}[/tex]
[tex]$=\frac{150}{4}[/tex]
[tex]$=\frac{75}{2}[/tex]
Average rate of change of the function [tex]=\frac{75}{2}[/tex]
