Newton\'s Law of Cooling states that the rate of cooling of an object is proport

Question

Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached 190 F and is placed on a table in a room where the temperature is 65 F. If u (t) is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that

This could be solved as a separable differential equation. Another method is to make the change of variable y = u - 65.
If the temperature of the turkey is 125 F after half an hour, what is the temperature after 20 min?

Pick one of the following:

A. t = 137 F

B. t = 142 F

C. t = 113 F

D. None of the above

E. t = 230 F

Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached 190 F and is placed on a table in a room where the temperature is 65 F. If u (t) is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that dU/dt = k(u - 65) This could be solved as a separable differential equation. Another method is to make the change of variable y = u - 65. If the temperature of the turkey is 125 F after half an hour, what is the temperature after 20 min? Pick one of the following: A. t = 137 F B. t = 142 F C. t = 113 F D. None of the above E. t = 230 F

Explanation / Answer

Log (u-65) = kt + log (190-65) Log (u-65) = kt + log (125) at t = 30 u = 125 therefore k = log(60/125) / 30 at t= 20 mins B. t = 142 F

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