Question

30 POINTS! 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)

Answer 1

Part a)
section Afavg=4(2)2−4(2)12−1=8section B favg=4(2)4−4(2)34−3=32
Part b)
The rate of change is greater between x = 3 and x = 4 than between x = 2 and x =1 because an exponential function's rate of change is increasing, unlike a linear function which has a a constant rate of change.