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Guests are arriving for a show when the theater manager realizes he forgot to turn...

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Basic Math

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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 F in the theater a 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 F until 3 00 p m What calculations did the theater manager make What was the temperature at 2 15 p m Hint a 201 b 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 78 76 73 72 71 70 70 79 What was the average rate of change after 3 00 p m until the temperature reached 70 F Why was the manager so far off in his prediction Hint b

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