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Consider a 2500-gallon capacity tank of water that contains 100 gallons of water in which 10...

Consider a 2500-gallon capacity tank of water that contains 100 gallons of water in which 10 pounds of salt are dissolved. Suppose that water with a salt concentration of 2 pounds per gallon enters the tank at a rate of 6 gallons per minute, is well-stirred, and the mixture leaves the tank at 5 gallons per minute. (a) Set up and solve the initial value problem to find the amount of salt in the tank as a function of time. Use this function to determine the amount of salt in the tank after 1 day (two decimal place rounding of your answer). (5 pts) (b) Suppose that, actually, the pump moving the mixture out of the tank is damaged and that the mixture is leaving the tank at 8 gallons per minute. (Water is still coming in at 6 gallons per minute.) Set up and solve this problem and then determine how long it takes for the tank to completely drain. What is the amount of salt in the tank at the half-way point? (4 pts

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