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madisontrosclair2
madisontrosclair2
22.04.2020 • 
Mathematics

A cold beer is heating up at a rate proportional to the difference between room temperature and the temperature of the beer. Denote by y(t) the temperature difference, i.e. y(t)=R-b(t), where R is room temperature and b(t) is beer temperature in degrees Fahrenheit. Here t is the time elapsed since the beer is poured, measured in minutes. The cooling of the beer is governed by the equation =ky(t) where k is a constant. (a) (3 points) Differentiate y(t), and then plug in y'(t) and y(t) to the above equation and check that both sides of the equation are equal. (b) (3 points) Now suppose that when the beer is poured, it is at 35 degrees. 10 minutes later, it is at 55 degrees. Room temperature R throughout is 75 degrees Fahrenheit. Use this information to figure out the unknown constants C and k and to determine the temperature of the beer b(t) as a function of time. (c) (3 points) At what time will the temperature of the beer be 70 degrees?

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