Intermediate Algebra (11th edition)

OBJECTIVE 5 Solve problems involving average rate of change.The slope

formula applied to any two points on a line gives the average rate of changeiny per

unit change inx, where the value ofy depends on the value ofx.

For example, suppose the height of a boy increased from 60 to 68 in. between the

ages of 12 and 16, as shown in FIGURE 22.

154 CHAPTER 3 Graphs, Linear Equations, and Functions

Change in height y Change in age x

12 13 14 15 16

70 68 66 64 62 60 x

y

Age (in years)

Height (in inches)

Growth Rate

1 yr

2 in. 0

FIGURE 22

2000 2001 2002

(2000, 690)

(2005, 980)

2003 2004 2005

Hours (per person)

Source: Veronis Suhler Stevenson.

Watching Cable and Satellite TV

Year

500 0

600

700

800

900

1000

FIGURE 23

To find the average rate of change, we need two pairs of data. From the graph,

we have the ordered pairs and We use the slope formula.

This means that the average time per person spent watching cable and satellite TV

increasedby 58 hr per year from 2000 to 2005.

average rate of change =

980 - 690

2005 - 2000

=

290

5

= 58

1 2000, 690 2 1 2005, 980 2.

A positive slope indicates an increase.

NOW TRY

NOW TRY
EXERCISE 9
Americans spent an average of
828 hr in 2002 watching cable
and satellite TV. Using this
number for 2002 and the num-
ber for 2000 from the graph in
FIGURE 23, find the average
rate of change from 2000 to

How does it compare
with the average rate of
change found in Example 9?

NOW TRY ANSWER

69 hr per yr; It is greater than
the average rate of change from
2000 to 2005.

Interpreting Slope as Average Rate of Change

The graph in FIGURE 23approximates the average number of hours per year spent

watching cable and satellite TV for each person in the United States from 2000 to

2005. Find the average rate of change in number of hours per year.

EXAMPLE 9

The boy may actually have grown more than 2 in. during some years and less than

2 in. during other years. If we plotted ordered pairs (age, height) for those years and

drew a line connecting any two of the points, the average rate of change would likely

be slightly different than that found above. However using the data for ages 12 and

16, the boy’s averagechange in height was 2 in. per year over these years.

68 - 60

16 - 12

=

8

4

= 2 in. Boy’s average growth rate (or average

change in height) per year