What is the average rate of change of the function f (x) = 2_((3)^x) from x = 2 to x = 4?

Question

What is the average rate of change of the function f (x) =
`2_((3)^x)` from x = 2 to x = 4?

Answer 1

the average rate of f(x) from x=a to x=b is the slope from (a,f(a)) to (b,f(b)) or
`(f(b)-f(a))/(b-a)`

for this problem

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

from x=2 to x=4

find f(2) and f(4)

`f(2)=2(3)^2=2(9)=18`

`f(4)=2(3)^4=2(81)=162`

so average rate of change from x=2 to x=4 is

`(f(4)-f(2))/(4-2)=(162-18)/(4-2)=(144)/(2)=72`

the average rate of change from x=2 to x=4 is 72