(Solved): 10. A tank initially contains 50 lbs. of salt dissolved in 100 gallons of water. Water containi ...

10. A tank initially contains 50 lbs. of salt dissolved in 100 gallons of water. Water containing $$2\mathrm{lbs}/\mathrm{gal}$$ of salt enters the tank at $$3\mathrm{gal}/\min$$ and the mixed solution is drained at the same rate. (a) Find $$\mathrm{A}(\mathrm{t})=$$ amount of salt in the tank at time t. (b) Find the limit of $$\mathrm{A}(\mathrm{t})$$ at $$\mathrm{t}$$ approaches infinity.