Problems #1 and #4

For Newton's Law of Cooling,set-up the differential equation and solve. Find the constant of proportionality and answer the question to the problem as applicable.

T?=?k(T?Tm)

4.2 Exercises A thermometer is moved from a room where the temperature is 70F to a freezer where the tem- perature is 12F. After 30 seconds the thermometer reads 40F. What does it read after 2 minutes? A uid initially at 100C is placed outside on a day when the temperature is 10C, and the temperature of the uid drops 20C in one minute. Find the temperature T (t) of the uid for t > 0. At 12:00 PM a thermometer reading 10F is placed in a room where the temperature is 70F. It reads 56 when it's placed outside, where the temperature is 5F, at 12:03. What does it read at 12:05 PM? A thermometer initially reading 212F is placed in a room where the temperature is 70F. After 2 minutes the thermometer reads 125F. (a) What does the thermometer read after 4 minutes? (b) When will the thermometer read 72F? (0) When will the thermometer read 69F? An object with initial temperature 150C is placed outside, where the temperature is 35C. Its temperatures at 12: 15 and 12:20 are 120C and 90C, respectively. (a) At what time was the object placed outside? (b) When will its temperature be 40C? An object is placed in a room where the temperature is 20C. The temperature of the object drops by 5C in 4 minutes and by 7C in 8 minutes. What was the temperature of the object when it was initially placed in the room? A cup of boiling water is placed outside at 1:00 PM. One minute later the temperature of the water is 152F. After another minute its temperature is 112F. What is the outside temperature? A tank initially contains 40 gallons of pure water. A solution with 1 gram of salt per gallon of water is added to the tank at 3 gal/min, and the resulting solution dranes out at the same rate. Find the quantity Q(t) of salt in the tank at time t > 0