Atank originally contains 100 gallon of fresh water. then the water containing 0.5 lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. after 10 mins, the processed is stopped, fresh water is poured into the tank at a rate of 10 gal/min, with the mixture again leaving at the same rate. (a) find the amount of salt in the tank at any time t in the first 10 mins (i. e: before the fresh water was poured in the tank. (b) find the amount of salt in the tank at the end of an additional 10 min (hint: let s(t) be the amount of salt in the first 10 mins, and let x(t) be the amount of salt in the tank after the first 10 mins. then your initial condition for x(t) will be x(0) = s(10)) (c) find the limiting amount of salt in the tank as t o