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: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 = 16Again, 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 = 64Part 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)