Given the function f(x) = 5x, section a is from x = 0 to x = 1 and section b is from x = 2 to x = 3.

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)

Are you sure you have f(x)=5x right? Because the rate of change for a linear function is constant, which makes the assignment a bit moot.

So f(x) = 5^x.

We'll need f(0)=1, f(1)=5, f(2)=25 and f(3)=125.

Rate of change in [0,1]: dy/dx = f(1)-f(0) / (1-0) = 5
Rate of change in [2,3]: dy/dx = f(3)-f(2) / (3-2) = 100

The rate of change in the second section is 20 times higher than the first. This is because f(x) is an exponential function.