Exercise 3 Page 79 - 3. Rate of Change and Slope - McGraw Hill Glencoe Algebra 2, 2012

a We are given a graph that shows the number of digital still cameras and film cameras sold by Yellow Camera Stores in recent years.

The average rate of change

r

can be found using the following formula.

r = \frac{change in y}{change in x} = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

In the formula,

y

represents the number of cameras and

x

represents the years. Notice that there were

20

thousand digital cameras sold in

2004

and

75

thousand sold in

2009 .

Let's substitute the values into the formula and find the average rate of change.

r = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

SubstitutePoints

Substitute $(2004, 20)$ & $(2009, 75)$

r = \frac{7 5 - 2 0}{2 0 0 9 - 2 0 0 4}

SubTerms

Subtract terms

r = \frac{5 5}{5}

CalcQuot

Calculate quotient

r = 11

The average rate of change of the number of digital cameras is about

11000

per year.

b We will find the average rate of change of the number of film cameras as in Part A. This time, there were

60

thousand digital cameras sold in

2004

and

35

thousand sold in

2009 .

Let's substitute the values into the formula and find the average rate of change.

r = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

SubstitutePoints

Substitute $(2004, 60)$ & $(2009, 35)$

r = \frac{3 5 - 6 0}{2 0 0 9 - 2 0 0 4}

SubTerms

Subtract terms

r = \frac{- 2 5}{5}

MoveNegNumToFrac

Put minus sign in front of fraction

r = - \frac{2 5}{5}

CalcQuot

Calculate quotient

r = - 5

Thus, the average rate of change for the number of film cameras is about

- 5000

per year.

c The positive rate in Part A represents an increase in sales of digital cameras. The negative rate in Part B represents a decrease in sales of film cameras.