Answer: 240
Step-by-step explanation:
The average rate of a function f(x) is interval [a,b] is given by :-
[tex]R=\dfrac{f(b)-f(a)}{b-a}[/tex]
Now, the given function : [tex]F(x)=4(5)^x[/tex]
Interval : [1,3]
Now, the average rate of change over the interval [1, 3] is given by :-
[tex]R=\dfrac{F(3)-F(1)}{3-1}\\\\=\dfrac{4(5)^3-4(5)^1}{2}\\\\=\dfrac{4(5^3-5)}{2}\\\\=\dfrac{4(125-5)}{2}=240[/tex]
Hence, the average rate of the change of the given function over the interval [1, 3] = 240
