Explanation Given Information: The cost in dollars of Dig-It brand snow shovels is defined by c ( t ) = 3.5 sin [ 2 π ( t − 0.75 ) ] where t is the number of years since January 1 , 2010 . Formula Used: The chain rule is being used which can be represented with the following formula: d d x ( sin u ) = d d x ( sin u ) ⋅ d u d x The following derivative formula is being used: d d x ( sin x ) = cos x Calculation: Consider the function c ( t ) = 3.5 sin [ 2 π ( t − 0.75 ) ] . Determine the derivative with respect to t. d d t 3.5 sin [ 2 π ( t − 0.75 ) ] Apply the chain rule. d d t 3.5 sin [ 2 π ( t − 0.75 ) ] = 3.5 d d t sin [ 2 π ( t − 0.75 ) ] d d t 3.5 sin [ 2 π ( t − 0.75 ) ] = 3.5 × 2 π cos [ 2 π ( t − 0

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 16.2, Problem 57E

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To calculate: The rate at which cost in dollars per week is increasing each October 1 when the cost in dollars of Dig-It brand snow shovels is defined by c(t)=3.5sin[2π(t−0.75)] where t is the number of years since January 1,2010.

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Chapter 16.2, Problem 56E

Chapter 16.2, Problem 58E

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Chapter 16 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

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 cost in dollars per week is increasing each October 1 when the cost in dollars of Dig-It brand snow shovels is defined by c ( t ) = 3.5 sin [ 2 π ( t − 0.75 ) ] where t is the number of years since January 1 , 2010 .

Solution Summary: The author calculates the rate at which cost per week is increasing each October 1 when the cost in dollars of Dig-It brand snow shovels is defined by c(t)=3.5

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To calculate: The rate at which cost in dollars per week is increasing each October 1 when the cost in dollars of Dig-It brand snow shovels is defined by c(t)=3.5sin[2π(t−0.75)] where t is the number of years since January 1,2010.

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Chapter 16 Solutions