Final answer:
The average rate of change for Section A (from x = 1 to x = 2) of the function f(x) = 4(2)^x is 8, and for Section B (from x = 3 to x = 4), it is 32.
Step-by-step explanation:
The student is asking how to find the average rate of change of the function f(x) = 4(2)x in two different sections: Section A (from x = 1 to x = 2) and Section B (from x = 3 to x = 4).
To calculate the average rate of change of a function between two points, we use the formula:
Average rate of change = ∆f / ∆x = (f(x2) - f(x1)) / (x2 - x1)
For Section A:
f(1) = 4(2)1 = 8
f(2) = 4(2)2 = 16
Average rate of change for Section A = (16 - 8) / (2 - 1) = 8
For Section B:
f(3) = 4(2)3 = 32
f(4) = 4(2)4 = 64
Average rate of change for Section B = (64 - 32) / (4 - 3) = 32
Therefore, the average rate of change for Section A is 8, and for Section B, it is 32.