Question

What is the average rate of change of the function f(x)=480(0.3)× from x=1 to x=5

Answer 1

What is the average rate of change of the function f(x)=480(0.3)x from x = 1 to x = 5? answer: -35.7084

Answer 2

The average rate of change(A(x)) of a function f(x) from a to b as;

`A(x) = (f(b)-f(a))/(b-a)`

Given the function:
`f(x) = 480(0.3)^x`

For x =1 ,

`f(x) = 480(0.3)^1 = 480\cdot 0.3 = 144`

and for x=5

`f(x) =480(0.3)^5 = 480 \cdot 0.00243= 1.1664`

then;

the average rate of change of a function A(x)=
`(f(5)-f(1))/(5-1)` or

`A(x) =(1.1664-144)/(4)= (-142.8336)/(4)= -35.7084`

Therefore, the average rate of change of the given function from x=1 to x=5 is; -35.7084