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. (4 points) 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. (6 points) (10 points)

Answer 1

Section A = 18

Section B = 288

Section B is 16 times greater than A

Explanation:

Given the function :

g(x) = 6(4)^x

x = 0 to x = 1

At x = 0

g(0) = 6(4)^0 = 6(1) = 6

At x = 1

g(1) = 6(4)*1 = 24

Average rate of change for Section A = g(1) - g(0) = 24 - 6 = 18

Section B ;

x = 2 ; x = 3

g(x) = 6(4)^x

x = 2 to x = 3

At x = 2

g(0) = 6(4)^2 = 6 * 16 = 96

At x = 3

g(1) = 6(4)^3 = 6(4*4*4) = 384

Average rate of change for Section B = g(3) - g(2) = 384 - 96 = 288

Number of times B is greater than A

Section B / section A = 288 / 18 = 16 times