2. A tank starts out holding 30 gallons of pure water. A sugary solution, which contains 5 grams of sugar per gallon, enters the tank at the rate of 2 gallons per minute. The contents of the tank are continuously mixed and pumped out of the tank at the rate of 2 gallons per minute. (a) What volume of liquid is contained in the tank at any given time? Why? (b) How many grams of sugar enter the tank every minute? (e) Let S(t) denote the number of grams of sugar in the tank after t minutes. What is S(0)? What is the concentration of sugar (in grams per gallon) after t minutes, in terms of S(t)? (d) Since the contents of the tank are pumped out at a rate of 2 gallons per minute, how many grams of sugar leave the tank each minute, in terms of S(t)? (e) Write a differential equation that expresses the total rate of change S' (t) in terms of S(t). (f) Find an explicit formula for S(t). (g) What happens to S(t) after a very long time? Explain how you could have predicted this without explicitly solving the differential equation.

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2 a tank starts out holding 30 gallons of pure water a sugary solution

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2. A tank starts out holding 30 gallons of pure water. A sugary solution, which contains 5 grams of sugar per gallon, enters the tank at the rate of 2 gallons per minute. The contents of the tank are continuously mixed and pumped out of the tank at the rate of 2 gallons per minute. (a) What volume of liquid is containe