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.

12

step-by-step explanation: