### Home > INT3 > Chapter 8 > Lesson 8.2.2 > Problem 8-83

Guests are arriving for a show when the theater manager realizes he forgot to turn on the air conditioning. The guests are very hot and uncomfortable. At 2:04 p.m. the manager turns on the air conditioning. It is 85ºF in the theater. Homework Help ✎

At 2:15 p.m. the manager announces that he has bad news. Using average rate of change he predicts the theater will not cool off to a comfortable 70ºF until 3:00 p.m. What calculations did the theater manager make? What was the temperature at 2:15 p.m.?

As the air conditioner continued cooling, the manager recorded these actual temperatures:

Time of day (p.m.)

2:04

2:15

2:24

2:32

2:37

2:53

3:01

3:18

3:27

3:40

Temperature (°F)

85

79

78

76

73

72

71

70

70

What was the average rate of change after 3:00 p.m. until the temperature reached 70ºF? Why was the manager so far off in his prediction?

By looking at the table, the temperature dropped 2° in 26 minutes.