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> 0k> 0 be the constant of proportionality. assume the coffee has a temperature of 200 degrees fahrenheit when freshly poured, and 1 minute later has cooled to 185 degrees in a room at 68 degrees.

(a) write an initial value problem for the temperature t of the coffee, in fahrenheit, at time t in minutes. your answer will contain the uknown constant k :
dtdt=

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t(0)=

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(b) solve the initial value problem in part (a). your answer will contain the unknown constant k .
t(t)=

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(c) determine the value of the constant k
k=

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minutes.

(d) determine when the coffee reaches a temperature of 150 degrees.

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minutes.