Explanation Given information: A Cup of coffee at 90 ° C is put into a 20 ° C room when t = 0 . The coffee’s temperature is changing at a rate of r ( t ) = − 7 ( 0.9 t ) ° C per minute, where t is in minutes. Concept used: The rate of change of coffee temperature is r ( t ) = − 7 ( 0.9 t ) ° C . Calculation: The temperature of cup of coffee is 90 ° C . The room temperature is 20 ° C at t = 0 . The rate of change of coffee temperature is r ( t ) = − 7 ( 0.9 t ) ° C . The temperature of cup of coffee decreases as t increases, because the room temperature is 20 ° C . The objective is to find temperature of cup of coffee at t = 10 . First find the decreased temperature after 10 minutes. The decreased temperature after 10 minutes of time is ∫ 0 10 r ( t ) d t = ∫ 0 10 [ − 7 ( 0.9 ) t ] d t = − 7 ∫ 0 10 [ ( 0

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ISBN: 9781119399353

Author: DA

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Chapter 5.5, Problem 1P

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To estimate the coffee’s temperature when t=10.

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To estimate the coffee’s temperature when t = 10 .

Solution Summary: The author calculates the temperature of a cup of coffee at 90°C. The rate of change of the coffee's temperature is r(t)=-7 (

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