Explanation Given Information: The Sales in bottles per day, of exclusive mass produced 2010 vintage Chateau Petit Mont Blanc follow the function s ( t ) = 4.5 e − 0.2 t sin ( 2 π t ) where t is the number of years since January 1 , 2010 . Formula Used: The product rule is used which can be represented with the following formula: d d x ( x ⋅ y ) = d d x ( x ) ⋅ y + x ⋅ d y d x The chain rule is used which can be represented with the following formula: d d x ( sin u ) = d d x ( sin u ) ⋅ d u d x The power rule is used which can be represented with the following formula: d d x ( x n ) = n ⋅ x n − 1 The following derivative formula is being used: d d x ( sin x ) = cos x Calculation: Consider the function s ( t ) = 4.5 e − 0.2 t sin ( 2 π t ) . Determine the derivative with respect to t. d d t 4.5 e − 0.2 t sin ( 2 π t ) Take out the constant term at the left of derivative. d d t 4.5 e − 0.2 t sin ( 2 π t ) = 4.5 d d t e − 0.2 t sin ( 2 π t ) Apply the product rule to the derivative function. 4.5 d d t e − 0.2 t sin ( 2 π t ) = 4.5 [ sin ( 2 π t ) ⋅ d d t e − 0.2 t + e − 0.2 t ⋅ d d t sin ( 2 π t ) ] Consider the first expression sin ( 2 π t ) ⋅ d d t e − 0.2 t . Apply the power rule to determine the derivative. sin ( 2 π t ) ⋅ d d t e − 0.2 t = sin ( 2 π t ) ⋅ ( − 0.2 ) e − 0.2 t Consider the second expression e − 0.2 t ⋅ d d t sin ( 2 π t ) . Apply the chain rule to determine the derivative. e − 0.2 t ⋅ d d t sin ( 2 π t ) = e − 0

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

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Chapter 16.2, Problem 62E

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To calculate: The rate at which sales are rising or falling on January 1,2011 if the Sales in bottles per day, of exclusive mass produced 2010 vintage Chateau Petit Mont Blanc follow the function s(t)=4.5e−0.2tsin(2πt) where t is the number of years since January 1,2010.

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Chapter 16.2, Problem 61E

Chapter 16.2, Problem 63E

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Chapter 16 Solutions

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

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The rate at which sales are rising or falling on January 1 , 2011 if the Sales in bottles per day, of exclusive mass produced 2010 vintage Chateau Petit Mont Blanc follow the function s ( t ) = 4.5 e − 0.2 t sin ( 2 π t ) where t is the number of years since January 1 , 2010 .

Solution Summary: The author calculates the rate at which sales are rising or falling on January 1,2011 if the Sales in bottles per day, of exclusive mass produced 2010 vintage Chateau Petit Mont Blanc follow the function sleft

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To calculate: The rate at which sales are rising or falling on January 1,2011 if the Sales in bottles per day, of exclusive mass produced 2010 vintage Chateau Petit Mont Blanc follow the function s(t)=4.5e−0.2tsin(2πt) where t is the number of years since January 1,2010.

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Chapter 16 Solutions