Question

Given the function f(x) = 4(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. (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)

(10 points)

Answer 1

Part A: Section A- 8, Section B- 32.

Part B: 4 times.

Explanation:

The function is given by .

Section A is from x = 1 to x = 2.

Now, f(1) = 4 × 2 = 8 and f(2) = 4 × 2 × 2 = 16

Again, section B is from x = 3 to x = 4.

Now, f(3) = 4 × 2 × 2 × 2 = 32 and f(4) = 4 × 2 × 2 × 2 × 2 = 64

Part A:

In section A, the average rate of change is = 8

And in section B, the average rate of change is = 32

Part B:

Therefore, the average rate of change of section B is greater than section A is (32 / 8 = 4)

Answer 2

Part A: Section A- 8, Section B- 32.

Part B: 4 times.

Explanation:

The function is given by
`f(x) = 4(2)^(x)`.

Section A is from x = 1 to x = 2.

Now, f(1) = 4 × 2 = 8 and f(2) = 4 × 2 × 2 = 16

Again, section B is from x = 3 to x = 4.

Now, f(3) = 4 × 2 × 2 × 2 = 32 and f(4) = 4 × 2 × 2 × 2 × 2 = 64

Part A:

In section A, the average rate of change is =
`(f(2) - f(1))/(2 - 1) = 16 - 8 = 8` (Answer)

And in section B, the average rate of change is =
`(f(4) - f(3))/(4 - 3) = 64 - 32 = 32` (Answer)

Part B:

Therefore, the number of times the average rate of change of section B is greater than section A is
`(32)/(8) = 4` (Answer)