Question

Given the function f(x)=5^2, 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

Part a) section A      4(2)2−4(2)12−1=8 section B  4(2)4−4(2)34−3=32Part 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.

Answer 2

Part A.
For an average rate of change you can just find Δf(x)/Δx using the points (x, f(x)).

x going from 0 --> 1

f(0) = 5^0
= 1
(0,1)

f(1) = 5^1
= 5
(1,5)

average rate of change Sect. A:
Δy/Δx = (5-1)/(1-0)
= 4

x going from 2-->3

f(2) = 5^2
= 25
(2, 25)

f(3) = 5^3
= 125
(3, 125)

average rate of change Sect. B:
Δy/Δx = (125-25)/(3-2)
= 100

Part B.
How many times greater is Sect B rate of change than Sect. A ?
100/4 = 25 times greater

Also, it is an exponential function so the rate of change is not constant. That is why the rates of change over the two sections are different.