Problem 2: Newton's cooling law provides the following differential equation for the cooling temperature T(t) (in F) of an object dT (t) dt = -k(T(t) - TA) (1) where TA is the ambient temperature and k is a positive constant. a) Find the solution T(t) of (1) for an initial temperature T(0) = To. b) When a chicken is removed from an oven, its temperature is measured at 300 F. Three minutes later its temperature is 200 F. How long will take for the chicken to cool off to a temperature of 100 F. The ambient temperature is 70 F. c) Validate your answer in b) by simulating the differential equation (1) with the given value of the ambient temperature and initial temperature.