Question

Ok this is really worth 90 pts, so can any body please help me on this.

Question 4 (Worth 90 points)
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)

Answer 1

Part 1 (or a if you prefer):

f(x) = 5^x

f(x) = 5^0 = 0

f(x) = 5^1 = 5

Use this formula to solve: f(b) - f(a)/b - a

5 - 0 / 1 - 0 = 5/1 = 5

--

f(x) = 5^2 = 25

f(x) = 5^3 = 125

125 - 25 / 3 - 2 = 100/1 = 100

Average rate of change:

Section A: 5

Section B: 100

Part 2 (or b if you prefer):

Section B is 20 times greater then A

This is because Section B is increasing in the equation. Thus, Section B is of greater value than Section A.

Hope this assists you and future students.

Answer 2

Part A:

f(x) = 5^x
f(x) = 5^0 = 0
f(x) = 5^1 = 5
Use this formula to solve: f(b) - f(a)/b - a
5 - 0 / 1 - 0 = 5/1 = 5
____________________

f(x) = 5^2 = 25
f(x) = 5^3 = 125
125 - 25 / 3 - 2 = 100/1 = 100

Average rate of change:
Section A: 5
Section B: 100

Part B:

Section B is 20 times greater then A
Why?
Because Section B is increasing in the equation. Thus, Section B is of greater value than Section A.