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)

Question

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Respuesta :

rani01654 rani01654 · Answer 1 · 2019-12-01T07:16:03+01:00

Answer:

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

Part B: 4 times.

Step-by-step explanation:

The function is given by [tex]f(x) = 4(2)^{x}[/tex].

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 = [tex]\frac{f(2) - f(1)}{2 - 1} = 16 - 8 = 8[/tex] (Answer)

And in section B, the average rate of change is = [tex]\frac{f(4) - f(3)}{4 - 3} = 64 - 32 = 32[/tex] (Answer)

Part B:

Therefore, the number of times the average rate of change of section B is greater than section A is [tex]\frac{32}{8} = 4[/tex] (Answer)