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

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

5th Edition

ISBN: 9780134872971

Author: Edwards, C., 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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MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

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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