A thermometer is taken from a room where the temperature is 24C to the outdoors, where the temperature is -1C. After one minute the thermometer reads 13C. (a) What will the reading on the thermometer be after 5 more minutes? (b) When will the thermometer read 0C? minutes after it was taken to the outdoors. A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the rate 4 L/min. (a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes: dy dt 4y 1000+4t (kg/min) y(0) = 60 kg. (b) Solve the initial value problem in part (a) y(t)=0kg. (c) Find the amount of salt in the tank after 3.5 hours. amount= (kg) (d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = 0 (kg/L) Note: You can earn partial credit on this problem. Water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the volume of water remaining. The tank initially contains 350 liters and 23 liters leak out during the first day. A. When will the tank be half empty? t days B. How much water will remain in the tank after 3 days? volume = OL Liters