Explanation Given: The temperature of a cup of coffee at time t is, T ( t ) = 70 + c e − k t (1) The initial temperature is T ( 0 ) = 200 ° F and after 3 minute the temperature is T ( 3 ) = 180 ° F and the value of t is 3. Formula used: The product rule of differentiation is, f ′ ( x ) = d d x [ f ( x ) . g ( x ) ] = f ( x ) ⋅ d d x g ( x ) + g ( x ) ⋅ d d x f ( x ) Calculation: Substitute 0 for t in the equation (1), T ( 0 ) = 70 + c e − k ⋅ 0 T ( 0 ) = 70 + c Substitute 200 for T ( 0 ) in the above equation to get the value of c , 200 = 70 + c 200 − 70 = c + 70 − 70 [ Subtract 70 from both sides ] c = 130 [ Simplify ] Substitute 130 for c and 3 for t in equation (1) to get the new equation, T ( 3 ) = 70 + 130 e − k ⋅ 3 T ( 3 ) = 70 + 130 e − 3 k Now, substitute 180 for T ( 3 ) in the above equation to get the value of k , 180 = 70 + 130 e − 3 k 180 − 70 = 70 + 130 e − 3 k − 70 [ Substitute 70 from both sides ] 110 130 = 130 e − 3 k 110 [ Divide both sides by 130 ] 13 11 = e 3 k x

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 5, Problem 6BM

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To find: The time for which the temperature of coffee reaches to 150°F from 200°F .

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Chapter 5, Problem 5BM

Chapter 6.1, Problem 1CQ

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Chapter 5 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

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The time for which the temperature of coffee reaches to 150 ° F from 200 ° F .

Solution Summary: The author explains how the temperature of a cup of coffee reaches to 150°F after 8.7 min. Substitute 200 for T(0) in the above

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To find: The time for which the temperature of coffee reaches to 150°F from 200°F .

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Chapter 5 Solutions