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Ready-made coffee comes out of the machine at 85 C. The room temperature is 20 C. After an hour, the coffee has cooled to 25

Ready-made coffee comes out of the machine at 85 C. The room temperature is 20 C. After an hour, the coffee has cooled to 25 C.

a) Determine the course of cooling over time with the help of an initial value problem.

b) After how many minutes does the drinking temperature reach 50 C?

Note: Use Newton's law of cooling for your modeling: The cooling rate is proportional to the difference between the coffee temperature and the ambient temperature.

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