Question

Problem 3. At midnight, the out down and stops producing heat. At F. Two hours later the tempera ght, the outside temperature is 20° F, when suddenly your furnace breaks ucing heat. At that time, the inside of your house has a temperature of 70 hours later the temperature inside your house has fallen to 50° F. (a): (6 points) Write down and solve the your home as a function of t hours since midnight. write down and solve the initial-value problem governing the temperature inside (b): (6 points) Assuming that your dog will start barking loudly in discomfort when the tem- perature in the house falls below 40° F, at what time of the night will everyone in your house be awakened by the dog?

Answer 1

(a e are ir mitial temperature of roo Taoutside tem berature-doF T) 50 F temperature eom after houYs Let T (In 'e) be temperature of om Cnfter thours of fur hale break-down Newtons Loo lin law

dT T-Ta dT TTA a T-T t+C aInTo--kE Pot n 50= C MT-30-k +nso T20 n -kt -kt Tao +o e Pot Ta) F

eak Rutin Tao t 50 Andwer Put T0F a 40 0+ so 3.58 haur 3heurs3S min regre time = 3:35 Am