Question

Given the function g(x) = 6(4)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

Answer 1

We are given the function:

g(x) = 6 (4)^x

Part A.

To get the average rate of change, we use the formula:

average rate of change = [g(x2) – g(x1)] / (x2 – x1)

Section A:

average rate of change = [6 (4)^1 – 6 (4)^0] / (1 – 0) = 18

Section B:

average rate of change = [6 (4)^3 – 6 (4)^2] / (3 – 2) = 288

Part B.

288 / 18 = 16

Therefore the average rate of change of Section B is 16 times greater than in Section A.

The average rate of change is greater between x = 2 to x = 3 than between x = 1 and x = 0 because an exponential function's rate of change increases with increasing x (not constant).