Question

Given the function h(x) = 3(2)x, 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.

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

Given:    h(x) = 3(2)ˣ,  Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.

To find : compare average rate of change of each section.

Solution:

h(x) = 3(2)ˣ,

Section A is from x = 1 to x = 2

h(1) = 3(2)¹  = 6

h(2) = 3(2)² = 12  

average rate of change of section A = (h(2) - h(1)) /( 2- 1)

= ( 12    - 6)/1

= 6

h(x) =3(2)ˣ,

Section B is from x = 3 to x = 4

h(3) = 3(2)³   = 24

h(4) = 3(2)⁴    = 48

average rate of change of section A = (h(4) - h(3)) /( 4- 3)

= ( 48    - 24 )/1

= 24

24/6

= 4  times is the average rate of section B compared to section A

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