A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the
temperature is 75 degrees F. (a) If the temperature of the turkey is 150 degrees F after half an hour, what is the temperature after 45 minutes?
(b) When will the turkey have cooled to 100 degrees F?
(a) Using Newton's Law of Cooling, , we have where T is temperature after T minutes. Separate by dividing both sides by T - 75 to get . Integrate both sides to get .
Since , we solve for C: So we get . Use T(30) = 150 to solve for k:
So
But choose Positive because T > 75. Temp of turkey can't go under.