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.)
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.