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58. Utility. The reaction R in pleasure units by a consumer receiving S units of a product can be modeled by the dif- ferential equation dR _ k S + 1' ds where k is a positive constant. a) Use separation of variables to solve the differential equation. b) Rewrite the solution in terms of the initial condition R(0) = 0. c) Explain why the condition R(0) = 0 is reasonable.

58. Utility. The reaction R in pleasure units by a consumer receiving S units of a product can be modeled by the dif- ferential equation dR _ k S + 1' ds where k is a positive constant. a) Use separation of variables to solve the differential equation. b) Rewrite the solution in terms of the initial condition R(0) = 0. c) Explain why the condition R(0) = 0 is reasonable.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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58. Utility. The reaction R in pleasure units by a consumer receiving S units of a product can be modeled by the dif- ferential equation dR _ k S + 1' ds where k is a positive constant. a) Use separation of variables to solve the differential equation. b) Rewrite the solution in terms of the initial condition R(0) = 0. c) Explain why the condition R(0) = 0 is reasonable.
Transcribed Image Text:58. Utility. The reaction R in pleasure units by a consumer receiving S units of a product can be modeled by the dif- ferential equation dR _ k S + 1' ds where k is a positive constant. a) Use separation of variables to solve the differential equation. b) Rewrite the solution in terms of the initial condition R(0) = 0. c) Explain why the condition R(0) = 0 is reasonable.
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