Answer:
The average rate of change(A(x)) of a function f(x) from a to b as;
[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex]
Given the function: [tex]f(x) = 480(0.3)^x[/tex]
For x =1 ,
[tex]f(x) = 480(0.3)^1 = 480\cdot 0.3 = 144[/tex]
and for x=5
[tex]f(x) =480(0.3)^5 = 480 \cdot 0.00243= 1.1664[/tex]
then;
the average rate of change of a function A(x)= [tex]\frac{f(5)-f(1)}{5-1}[/tex] or
[tex]A(x) =\frac{1.1664-144}{4}= \frac{-142.8336}{4}= -35.7084[/tex]
Therefore, the average rate of change of the given function from x=1 to x=5 is; -35.7084
