Question

Given the function h(x) = 4x, 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

the correct question is
Given the function
`h(x)= 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.

we know that
The "rate of change" is just the slope of the function in the section.
In Section A:
m=[f(b)-f(a)]/[b-a]
from x = 0 to x = 1
a=0
b=1
f(a) =
`4 ^(0) =1`
f(b) =
`4 ^(1) =4`
m=[f(b)-f(a)]/[b-a]------> m=[4-1]/[1-0]------> m=3

In Section B:
m=[f(b)-f(a)]/[b-a]
from x = 2 to x =3
a=2
b=3
f(a) =
`4 ^(2) =16`
f(b) =
`4 ^(3) =64`
m=[f(b)-f(a)]/[b-a]------> m=[64-16]/[3-2]------> m=48

Part A:
1) The average rate of change of Section A is 3
2)The average rate of change of Section B is 48

Part B:
3) The average rate of change of Section B is equal to 48 times greater the average rate of change of Section A.
This is because Section B is the increasing part of the equation