Objectives

Understand Rates of Change Identify rates from graphs

Vocabulary:

Rate

Slide 3- 1Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Slide 3- 2Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

RateA rate is a ratio that indicates how two quantities change with respect to each other.

Slide 3- 3Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example On March 4, Nichole rented a mini-van with a full tank of gas and 10,324 mi on the odometer. On March 9, she returned the mini-van with 10,609 mi on the odometer. If the rental agency charged Nichole $126 for the rental and needed 15 gal of gas to fill up the gas tank, find the following rates:

a) The car’s average rate of gas consumption, in miles per gallon.

b) The average cost of the rental, in dollars per day.

c) The car’s rate of travel, in miles per day.

Slide 3- 4Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example On March 4, Nichole rented a mini-van with a full tank of gas and 10,324 mi on the odometer. On March 9, she returned the mini-van with 10,609 mi on the odometer. If the rental agency charged Nichole $126 for the rental and needed 15 gal of gas to fill up the gas tank, find the following rates:

Solution a) The car’s average rate of gas consumption, in miles per gallon.

Rate, in miles per gallon 10,609 mi 10,324 mi

15 gal

28519 mi/gal

15

Slide 3- 5Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example On March 4, Nichole rented a mini-van with a full tank of gas and 10,324 mi on the odometer. On March 9, she returned the mini-van with 10,609 mi on the odometer. If the rental agency charged Nichole $126 for the rental and needed 15 gal of gas to fill up the gas tank, find the following rates:

Solution (continued) b) The average cost of the rental, in dollars per day.

Rate, in dollars per day 126 dolla

5

rs

days

25.20 dollars/day

Slide 3- 6Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Solution (continued)c) The car’s rate of travel, in miles per day.

Rate, in miles per day

Example On March 4, Nichole rented a mini-van with a full tank of gas and 10,324 mi on the odometer. On March 9, she returned the mini-van with 10,609 mi on the odometer. If the rental agency charged Nichole $126 for the rental and needed 15 gal of gas to fill up the gas tank, find the following rates:

285 mi

5 days

57 mi/day

Slide 3- 7Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example Wanda’s Hair Salon has a graph displaying data from a recent day of work.

a) What rate can be determined from the graph?

b) What is that rate?

Solution

a) We can find the rate Number of haircuts per hour.

b)

1 2 3 4 5

10 haircuts 2 haircuts 8 haircuts2 haircuts per hour.

5 : 00 1: 00 4 hours