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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)

User Laalto
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2 Answers

3 votes

Answer:

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)

User Tekknolagi
by
8.1k points
4 votes

Answer:

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)

User WebDude
by
8.3k points

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