Program Explanation Given information: The temperature of the body is 75 ° F at 12 noon and the room temperature is 70 ° C . The another condition is the temperature of the body is 80 ° C at 1 pm . The initial body temperature is 98.6 ° C . Calculation: Consider the standard equation of Newton’s law of cooling as follows, d T d t = − k ( T − A ) Here, A is the temperature of the outside. The room temperature is 70 ° C therefore, the value of A = 70 . Separate the variables of the above differential equations, as follows: d T ( T − 70 ) = − k d t Integrate the equation on both the sides. ∫ d T ( T − 70 ) = − ∫ k d t Evaluate the above integral as follows, ln c ( T − 70 ) = − k t Further evaluate the above equation for the value of T , as follows: T = 70 + c e − k t ........(1) Apply the initial condition that the temperature of body is 98.6 ° F at t = 0 to obtain the value of c . T = 70 + c e − k t 98.6 = 70 + c e − k ( 0 ) 28.6 = c c = 28.6 Now substitute 28.6 for c in equation (1) to obtain the temperature function. T = 70 + 28.6 e − k t ........(2) I t is given that the temperature of the body is 80 ° C at 12 noon and the temperature of the body is 75 ° F at 1 pm . Consider t = a at 12 noon. Apply the boundary condition that temperate of the body is 80 ∘ F at t = a to obtain the value of k . Substitute a for t and 80 ∘ F for T in equation (2) to obtain the value of k . 80 = 70 + 28.6 e − k a 10 = 28.6 e − k a 10 28.6 e − k a = 1 Therefore, the equation is as follows, 10 28

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

Publisher: PEARSON

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Chapter 1.4, Problem 65P

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Program Description: Purpose of the problem is to find the time of death.

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Chapter 1.4, Problem 64P

Chapter 1.4, Problem 66P

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Chapter 1 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

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Ch. 1.1 - Prob. 11P Ch. 1.1 - Prob. 12P Ch. 1.1 - Prob. 13P Ch. 1.1 - Prob. 14P Ch. 1.1 - Prob. 15P Ch. 1.1 - Prob. 16P Ch. 1.1 - Prob. 17P Ch. 1.1 - Prob. 18P Ch. 1.1 - Prob. 19P Ch. 1.1 - Prob. 20P Ch. 1.1 - Prob. 21P Ch. 1.1 - Prob. 22P Ch. 1.1 - Prob. 23P Ch. 1.1 - Prob. 24P Ch. 1.1 - Prob. 25P Ch. 1.1 - Prob. 26P Ch. 1.1 - Prob. 27P Ch. 1.1 - Prob. 28P Ch. 1.1 - Prob. 29P Ch. 1.1 - Prob. 30P Ch. 1.1 - Prob. 31P Ch. 1.1 - Prob. 32P Ch. 1.1 - Prob. 33P Ch. 1.1 - Prob. 34P Ch. 1.1 - Prob. 35P Ch. 1.1 - Prob. 36P Ch. 1.1 - Prob. 37P Ch. 1.1 - Prob. 38P Ch. 1.1 - Prob. 39P Ch. 1.1 - Prob. 40P Ch. 1.1 - Prob. 41P Ch. 1.1 - Prob. 42P Ch. 1.1 - Prob. 43P Ch. 1.1 - Prob. 44P Ch. 1.1 - Prob. 45P Ch. 1.1 - Prob. 46P Ch. 1.1 - Prob. 47P Ch. 1.1 - Prob. 48P Ch. 1.2 - Prob. 1P Ch. 1.2 - Prob. 2P Ch. 1.2 - Prob. 3P Ch. 1.2 - Prob. 4P Ch. 1.2 - In Problems 1 through 10, find a function y=f(x)...Ch. 1.2 - Prob. 6P Ch. 1.2 - Prob. 7P Ch. 1.2 - Prob. 8P Ch. 1.2 - Prob. 9P Ch. 1.2 - Prob. 10P Ch. 1.2 - 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Prob. 10P Ch. 1.3 - Prob. 11P Ch. 1.3 - Prob. 12P Ch. 1.3 - Prob. 13P Ch. 1.3 - Prob. 14P Ch. 1.3 - Prob. 15P Ch. 1.3 - Prob. 16P Ch. 1.3 - Prob. 17P Ch. 1.3 - Prob. 18P Ch. 1.3 - Prob. 19P Ch. 1.3 - Prob. 20P Ch. 1.3 - Prob. 21P Ch. 1.3 - Prob. 22P Ch. 1.3 - Prob. 23P Ch. 1.3 - Prob. 24P Ch. 1.3 - Prob. 25P Ch. 1.3 - Prob. 26P Ch. 1.3 - Prob. 27P Ch. 1.3 - Prob. 28P Ch. 1.3 - Verify that if c is a constant, then the function...Ch. 1.3 - Prob. 30P Ch. 1.3 - Prob. 31P Ch. 1.3 - Prob. 32P Ch. 1.3 - Prob. 33P Ch. 1.3 - (a) Use the direction field of Problem 5 to...Ch. 1.3 - Prob. 35P Ch. 1.4 - Prob. 1P Ch. 1.4 - Prob. 2P Ch. 1.4 - Prob. 3P Ch. 1.4 - Prob. 4P Ch. 1.4 - Prob. 5P Ch. 1.4 - Prob. 6P Ch. 1.4 - Prob. 7P Ch. 1.4 - Prob. 8P Ch. 1.4 - Prob. 9P Ch. 1.4 - Prob. 10P Ch. 1.4 - Prob. 11P Ch. 1.4 - Prob. 12P Ch. 1.4 - Prob. 13P Ch. 1.4 - Prob. 14P Ch. 1.4 - Prob. 15P Ch. 1.4 - Prob. 16P Ch. 1.4 - Prob. 17P Ch. 1.4 - Prob. 18P Ch. 1.4 - Prob. 19P Ch. 1.4 - Prob. 20P Ch. 1.4 - Prob. 21P Ch. 1.4 - 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Prob. 62P Ch. 1.4 - Prob. 63P Ch. 1.4 - (The clepsydra, or water clock) A 12 h water clock...Ch. 1.4 - Prob. 65P Ch. 1.4 - Prob. 66P Ch. 1.4 - Prob. 67P Ch. 1.4 - Figure 1.4.11 shows a bead sliding down a...Ch. 1.4 - Prob. 69P Ch. 1.5 - Prob. 1P Ch. 1.5 - Prob. 2P Ch. 1.5 - Prob. 3P Ch. 1.5 - Prob. 4P Ch. 1.5 - Prob. 5P Ch. 1.5 - Prob. 6P Ch. 1.5 - Prob. 7P Ch. 1.5 - Prob. 8P Ch. 1.5 - Prob. 9P Ch. 1.5 - Prob. 10P Ch. 1.5 - Prob. 11P Ch. 1.5 - Prob. 12P Ch. 1.5 - Prob. 13P Ch. 1.5 - Prob. 14P Ch. 1.5 - Prob. 15P Ch. 1.5 - Prob. 16P Ch. 1.5 - Prob. 17P Ch. 1.5 - Prob. 18P Ch. 1.5 - Prob. 19P Ch. 1.5 - Prob. 20P Ch. 1.5 - Prob. 21P Ch. 1.5 - Prob. 22P Ch. 1.5 - Prob. 23P Ch. 1.5 - Prob. 24P Ch. 1.5 - Prob. 25P Ch. 1.5 - Prob. 26P Ch. 1.5 - Prob. 27P Ch. 1.5 - Prob. 28P Ch. 1.5 - Prob. 29P Ch. 1.5 - Prob. 30P Ch. 1.5 - Prob. 31P Ch. 1.5 - Prob. 32P Ch. 1.5 - Prob. 33P Ch. 1.5 - Prob. 34P Ch. 1.5 - Prob. 35P Ch. 1.5 - Prob. 36P Ch. 1.5 - Prob. 37P Ch. 1.5 - Prob. 38P Ch. 1.5 - Prob. 39P Ch. 1.5 - 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Show that the substitution...Ch. 1.6 - Prob. 57P Ch. 1.6 - Prob. 58P Ch. 1.6 - Solve the differential equation dydx=xy1x+y+3 by...Ch. 1.6 - Prob. 60P Ch. 1.6 - Prob. 61P Ch. 1.6 - Prob. 62P Ch. 1.6 - Prob. 63P Ch. 1.6 - Prob. 64P Ch. 1.6 - Prob. 65P Ch. 1.6 - Prob. 66P Ch. 1.6 - Prob. 67P Ch. 1.6 - Prob. 68P Ch. 1.6 - Prob. 69P Ch. 1.6 - As in the text discussion, suppose that an...Ch. 1.6 - Prob. 71P Ch. 1.6 - Prob. 72P Ch. 1 - Prob. 1RP Ch. 1 - Prob. 2RP Ch. 1 - Prob. 3RP Ch. 1 - Prob. 4RP Ch. 1 - Prob. 5RP Ch. 1 - Prob. 6RP Ch. 1 - Prob. 7RP Ch. 1 - Prob. 8RP Ch. 1 - Prob. 9RP Ch. 1 - Prob. 10RP Ch. 1 - Prob. 11RP Ch. 1 - Prob. 12RP Ch. 1 - Prob. 13RP Ch. 1 - Prob. 14RP Ch. 1 - Prob. 15RP Ch. 1 - Prob. 16RP Ch. 1 - Prob. 17RP Ch. 1 - Prob. 18RP Ch. 1 - Prob. 19RP Ch. 1 - Prob. 20RP Ch. 1 - Prob. 21RP Ch. 1 - Prob. 22RP Ch. 1 - Prob. 23RP Ch. 1 - Prob. 24RP Ch. 1 - Prob. 25RP Ch. 1 - Prob. 26RP Ch. 1 - Prob. 27RP Ch. 1 - Prob. 28RP Ch. 1 - Prob. 29RP Ch. 1 - Prob. 30RP Ch. 1 - Prob. 31RP Ch. 1 - Prob. 32RP Ch. 1 - Prob. 33RP Ch. 1 - Prob. 34RP Ch. 1 - Prob. 35RP Ch. 1 - Prob. 36RP

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Program Description: Purpose of the problem is to find the time of death.

Solution Summary: The author explains that the problem is to find the time of death. The initial body temperature is 98.6°C.

Program Description: Purpose of the problem is to find the time of death.

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Chapter 1 Solutions