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

f(x)=12(3)xf(x)=12(3)x

F(x)=12(3)ˣ

just find the slope

so for x=0
f(0)=12(3)⁰
f(0)=12(1)
f(0)=12
(0,12)

for x=5
f(5)=12(3)⁵
f(5)=12(243)
f(5)=2916
(5,2916)

the slope between (x1,y1) and (x2,y2) is
(y2-y1)/(x2-x1)
given

(0,12) and (5,2916)
slope=(2916-12)/(5-0)=2904/5

the rate of change is 2904/5