A tank originally contains 10 gal of water with 1/2 lb of salt in solution. Water...

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A tank originally contains 10 gal of water with 1/2 lb of salt in solution. Water containing a salt concentration of 200 (10-t)2 (sin(t)+1) lb per gallon flows into the tank at a rate of 1 gal/ min, and the mixture is allowed to flow out of the tank at a rate of 2 gal/ min. The mixture is kept uniform by stirring. Let Q(t) (in lb) be the amount of salt in the tank after time t (in min). (i) How long (in min) will it take for the tank to become empty? (ii) Write the initial value problem for Q(t) (before the tank is empty) and solve it. A tank originally contains 10 gal of water with 1/2 lb of salt in solution. Water containing a salt concentration of 200 (10-t)2 (sin(t)+1) lb per gallon flows into the tank at a rate of 1 gal/ min, and the mixture is allowed to flow out of the tank at a rate of 2 gal/ min. The mixture is kept uniform by stirring. Let Q(t) (in lb) be the amount of salt in the tank after time t (in min). (i) How long (in min) will it take for the tank to become empty? (ii) Write the initial value problem for Q(t) (before the tank is empty) and solve it.

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