A pork roast22 was taken out of a hardwood smoker when its internal temperature had reached 180◦F and it was allowed to rest in a 75◦F house for 20 minutes after which its internal temperature had dropped to 170◦F. Assuming that the temperature of the roast follows Newton’s Law of Cooling (Equation 6.6),
(a) Express the temperature T (in ◦F) as a function of time t (in minutes). (b) Find the time at which the roast would have dropped to 140◦F had it not been carved and eaten.