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