Question

What is the average rate of change of the function on the interval from x = 0 to x = 5?

f(x)=1/2(3)^x

Answer 1

the average rate is 3^x/2

Answer 2

Average rate of change = 24.2

Explanation:

`f(x)=(1)/(2)3^x`

Average rate of change formula is on interval a to b is

`(f(b)-f(a))/(b-a)`

Given interval is x=0 to x=5

a=0 and b=5

Average rate =
`(f(5)-f(0))/(5-0)`

`f(0)=(1)/(2)3^0=\fracc{1}{2}=0.5`

`f(5)=(1)/(2)3^5=\frac{3^5}(2}=121.5`

Average rate =
`(f(5)-f(0))/(5-0)`

Average rate =
`(121.5-0.5)/(5)=24.2`

Average rate of change = 24.2