Question

Given the function g(x) = 6x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4. 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)

Answer 1

The function is: g ( x ) = 6^x
Section A: from x = 1 to x = 2
g ( 1 ) = 6, g ( 2 ) = 36
Average rate of change:
( 36 - 6 ) / ( 2 - 1 ) = 30 / 1 = 30
Section B : from x = 3 to x = 4
g ( 3 ) = 6^3 = 216, g ( 4 ) = 6 ^4 = 1296
Average rate of change:
( 1296 - 216 ) / ( 4 - 3 ) = 1080 / 1 = 1080
1080 : 30 = 36
Average rate of change of Section B is 36 times greater than the Section A.
This is because the function is exponential.