Answer: The average rate of change of function f(x) is -35.7084.
Explanation:
The given function is,
[tex]f(x)=480(0.3)^x[/tex]
Where to find the rate of change of function from x=1 to x=5.
Put x=1
[tex]f(1)=480(0.3)^{1}=144[/tex]
put x=5.
[tex]f(5)=480(0.3)^{5}=1.1664[/tex]
Rate of change is,
[tex]Slope=\frac{\text{Change is f(x)}}{\text{Change is x}}[/tex]
[tex]m=\frac{f(5)-f(1)}{5-1}[/tex]
[tex]m=\frac{1.1664-144}{4}[/tex]
[tex]m=\frac{-142.8336}{4}[/tex]
[tex]m=-35.7084[/tex]
Therefore the rate of change is -35.7084. It means the function f(x) decreases by 35.7084 units as x increases by 1 unit.
