Given the function f(x) = 2(3)^x, section a is from x = 0 to x = 1 and section b is from x = 2 to x = 3.

part a: find the average rate of change of each section.

part b: how many times greater is the average rate of change of section b than section a? explain why one rate of change is greater than the other.

i need with explanation

Average rate of change can be calculated by determining the rate of change at x = a, and at x = b

f’(x) =2 (3^x) ln(3)

f’(0) = 2 ln(3)

f’(1) = 6 ln(3)

f’(2) = 18 ln(3)

f’(3) = 54 ln(3)

Average:

at section A = [6 ln(3) – 2 ln(3)]/1 = 4 ln(3)

at section B = [54 ln(3) – 18 ln(3)]/1 = 36 ln(3)

section B is 9 times larger.

Based from the f’(x), f’(x) varies as the power of x. so the greater of value of x, the greater the rate of change.

answer4 to the second power is 16

and 4 to the third power is 64,