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 $85^\circ$F in the theater.

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 $70^\circ$F until 3:00 p.m. What calculations did the theater manager make? What was the temperature at 2:15 p.m.?

   Hint (a):

   Time of day (p.m.)	2:04	2:15	3:00
   Temperature ($^\circ{\text{F}}$)	$85$		$70$

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 ($^\circ$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 $70^\circ$F? Why was the manager so far off in his prediction?

   Hint (b):

   By looking at the table, the temperature dropped $2^\circ$ in $26$ minutes.