Explanation Formula used: Integrating factor: The integrating factor of the First-Order linear differential equation y ′ + f ( x ) y = g ( x ) is I ( x ) = e ∫ f ( x ) d x . Calculation: It is given that the model for weight loss or gain is d w d t + 0.005 w = 1 3 , 500 C where w ( t ) is, a person’s weight after t days consuming exactly C calories per day. Here, the person goes on a diet of 2,800 calories per day. Therefore the equation becomes, d w d t + 0.005 w = 2 , 800 3 , 500 d w d t + 0.005 w = 0.8 Find the integrating factor of the first order linear equation d w d t + 0.005 w = 0.8 where f ( t ) = 0.005 and g ( t ) = 0.8 . I ( w ) = e ∫ 0.005 d t = e 0.005 t Multiply both sides of the equation by the integrating factor. e 0.005 t d w d t + 0.005 e 0.005 t w = 0.8 e 0.005 t ( e 0.005 t w ) ′ = 0.8 e 0.005 t [ ∵ ( x y ) ′ = x y ′ + x ′ y ] Integrate both sides of the equation. ∫ ( e 0.005 t w ) ′ d w = 0.8 ∫ e 0.005 t d w e 0.005 t w = 0.8 ( e 0.005 t 0.005 ) + c e 0.005 t w = 160 e 0.005 t + c w = 160 + c e − 0

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

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Chapter 9.3, Problem 76E

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To find: How much will the person weigh after 90 days on the given diet, how long will the person take to lose 25 pounds and find limt→∞w(t).

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Chapter 9.3, Problem 75E

Chapter 9.3, Problem 77E

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Chapter 9 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 9.1 - Show that y=Cx+1 is the general solution of the...Ch. 9.1 - Prob. 2MP Ch. 9.1 - Prob. 3MP Ch. 9.1 - Prob. 4MP Ch. 9.1 - Prob. 5MP Ch. 9.1 - Prob. 1ED Ch. 9.1 - Prob. 2ED Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E

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How much will the person weigh after 90 days on the given diet, how long will the person take to lose 25 pounds and find lim t → ∞ w ( t ) .

Solution Summary: The author calculates how much the person will weigh after 90 days on the given diet, how long it will take to lose 25 pounds, and the integrating factor of the first-order linear equation.

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To find: How much will the person weigh after 90 days on the given diet, how long will the person take to lose 25 pounds and find limt→∞w(t).

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Chapter 9 Solutions