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8-83.
  1. 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 ✎

    1. 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.?

    2. 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.