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Newton's Law of Cooling.) Let T(t) be the temperature of an object in a room of fixed ambient Cemperature A. The rate of change of temperature is proportional to the difference between T and A, .e., T satisfies dT dt 1 = -k(T - A). (a) Find a general solution for T(t). (b) An iced tea at 5°C is placed in a cabana where the temperature is 35°C. After ten minutes the iced tea is at 10°C. What is the temperature of the drink after 40 minutes? (c) What happens as to in this model?

Newton's Law of Cooling.) Let T(t) be the temperature of an object in a room of fixed ambient Cemperature A. The rate of change of temperature is proportional to the difference between T and A, .e., T satisfies dT dt 1 = -k(T - A). (a) Find a general solution for T(t). (b) An iced tea at 5°C is placed in a cabana where the temperature is 35°C. After ten minutes the iced tea is at 10°C. What is the temperature of the drink after 40 minutes? (c) What happens as to in this model?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(Newton's Law of Cooling.) Let T(t) be the temperature of an object in a room of fixed ambient temperature A. The rate of change of temperature is proportional to the difference between T and A, i.e., T satisfies dT dt -k(T - A). (a) Find a general solution for T(t). (b) An iced tea at 5°C is placed in a cabana where the temperature is 35°C. After ten minutes the iced tea is at 10°C. What is the temperature of the drink after 40 minutes? (c) What happens as too in this model?
Transcribed Image Text:(Newton's Law of Cooling.) Let T(t) be the temperature of an object in a room of fixed ambient temperature A. The rate of change of temperature is proportional to the difference between T and A, i.e., T satisfies dT dt -k(T - A). (a) Find a general solution for T(t). (b) An iced tea at 5°C is placed in a cabana where the temperature is 35°C. After ten minutes the iced tea is at 10°C. What is the temperature of the drink after 40 minutes? (c) What happens as too in this model?
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