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Mathematics, 05.02.2021 22:00 marmar69

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 surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. Let k>0 be the constant of proportionality. Assume the coffee has a temperature of 200 degrees Fahrenheit when freshly poured, and 11 minutes later has cooled to 190 degrees in a room at 62 degrees. Required:
a. Write an initial value problem for the temperature T of the coffee, in Fahrenheit, at time t in minutes.
b. Solve the initial value problem in part (a).

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