Suppose a small metal object, initially at a temperature of 40 degrees, is immersed in a room which is held at the constant temperature of 70 degrees. It takes 2 minutes for the temperature of the object to reach 55 degrees. Required:
a. Calculate the heat transfer coefficient r , i. e. the constant of proportionality in the differential equation that describes Newton's law of cooling.
r =

b. Suppose now that the room temperature begins to vary; i. e. Troom(t) = 90 + sin(0.1 t) . Use Newton's law of cooling and the heat transfer coefficient you calculated in the previous step to compute the temperature of the object as a function of time. Suppose that T(0) = 70 . T(t)