1)Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at the same rate. Determine a differential equation for the amount of salt A(t) in the tank at time t0. What is A(0)?
2) Newton’s law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. An object at a temperature of 80 degree Celsius(C) placed in a refrigerator maintained at 5C. If the temperature of the object is 7C at 20 minutes after it is placed in the refrigerator, determine the time (in hours) it will take for the object to reach 10C.