Answer to Question #12237 in Other Math for joe
Let's assume that the turkey temperature decreases by the next law:
T(t) = c(T(t)-Tr)t,& (1)
T(t) = - c*Tr*t / (1-c*t), (2)
where T is the current turkey temperature, T0 is initial turkey temperature, Tr is the room temperature, c is the cooling coefficient and t is the time since turkey was taken out from the oven. Let's find c. We know that T0 = 185°F and after half an hour it decreased to 150°F. So,
(1) ==> 150 = c(150-75)0.5 ==> c = 4 units/hour.
So, after 45 minutes the temperature of a turkey will be
(2) ==> T(3/4 hour) = - 4*75*3/4 / (1-4*3/4) =& 112.5°F.
B) When will the turkey cool to 100 degrees?
(1) ==> 100 = 4(100-75)t ==> t = 1 hour.
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