Reread Example 4 in Section 3.1 on the cooling of a cake that is taken out of an oven.

(a) Devise a mathematical model for the temperature of a cake while it is inside the oven based on the following assumptions: At t = 0 the cake mixture is at the room temperature of 70°; the oven is not preheated, so at t = 0, when the cake mixture is placed into the oven, the temperature inside the oven is also 70°; the temperature of the oven increases linearly until t = 4 minutes, when the desired temperature of 300° is attained; the oven temperature is a constant 300° for t ≥ 4.

(b) Use the Laplace transform to solve the initial-value problem in part (a).