Problem 21. Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its sur- roundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. The coffee has a temperature of 80°C when freshly poured, and 1 min later has cooled to 70°C, when the temperature outdoors is 0°C. (a) Write an initial value problem for this model. (b) Determine the time when the coffee reaches a temperature of 40°C. (Note: Begin the solution by stating your notation).
Problem 21. Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its sur- roundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. The coffee has a temperature of 80°C when freshly poured, and 1 min later has cooled to 70°C, when the temperature outdoors is 0°C. (a) Write an initial value problem for this model. (b) Determine the time when the coffee reaches a temperature of 40°C. (Note: Begin the solution by stating your notation).
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Transcribed Image Text:Problem 21. Newton's law of cooling states that the temperature of an object changes
at a rate proportional to the difference between its temperature and that of its sur-
roundings. Suppose that the temperature of a cup of coffee obeys Newton's law of
cooling. The coffee has a temperature of 80°C when freshly poured, and 1 min later
has cooled to 70°C, when the temperature outdoors is 0°C.
(a) Write an initial value problem for this model.
(b) Determine the time when the coffee reaches a temperature of 40°C.
(Note: Begin the solution by stating your notation).
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