Question

99 points ALGERBA 1 HELLP
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

PART A

The given equation is $3(2)^{x}$

When $x=1$, $h(1)=3 (2)^{1}=6$
When $x=2$, $h(2)=3 (2)^{2}= 12$
When $x=3$, $h(3)=3 (2)^{3} = 24$
When $x=4$, $h(4)=3 (2)^{4}=48$

Between $x=1$ and $x=2$ there is an increase by 12
Between $x=3$ and $x=4$ there is an increase by 24

PART B

The change in section B is twice the change in section A. This change is an exponential change indicated by the expression $2^{x}$ in the function. If we continue to check the rate of change between $x=5$ and $x=6$, we will discover that the change will be four times the rate of change between $x=3$ and $x=4$.