Question

Given the function f(x) = 5^x, 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)

Answer 1

Table of the graph:
x: 1 2 3
y: 5 25 125

Average Rate of Change =
`(y_(2)-y_(1) )/(x_(2) - x_(1) )`

Section A = 25-5/2-1 =20/1 =20
Section B = 125 - 25/ 3-2 = 100/1 = 100

So, Section B is 5 times greater than A.
Section B is greater because the slope of two points is greater than points in Section A.