Answer:
The average rate of change is 7.5
Step-by-step explanation:
The given exponential function is
[tex]f(x) = {2}^{x} + 3[/tex]
The average rate of change over a≤x≤b is given by
[tex] \frac{f(a) - f(b)}{a - b} [/tex]
Since we want to fine the average rate of change over 1≤x≤5, we have a=1 and b=5
[tex]\frac{f(1) - f(5)}{1 - 5} [/tex]
We plug into the functions to get:
[tex] \frac{ {2}^{1} + 3 - {2}^{5} - 3}{ - 4} [/tex]
Simplify
[tex]\frac{ {2} - 32}{ - 4} = \frac{ - 30}{ - 4} = 7.5[/tex]
