Problem 2. A yam at room temperature is put into an oven set to 400 degrees. Assume the oven's temperature is maintained at a constant 400, and assume the yam's temperature follows Newton's law of cooling. The temperature of the yam at time t is T(t). (a) What is the limit of T(t) as t goes to infinity? (b) If T(0) = 70 and T(20) = 300, find the formula for T(t). (c) Using the formula from part b, what do you expect the rate of temperature increase to be at t=40? (d) Compare your answer for (a) and (c). If T(t) is increasing and its limit at infinity is finite what would you expect happens to the limit of its derivative? Does that have to happen?

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