A tank initially contains 5 lb of salt dissolved in 1000 gal of water.

Problem 2. A tank initially contains 5 lb of salt dissolved in 1000 gal of water. A 2% brine solution (salty water) enters the tank at a rate of 3 gal/min, the resulting mixture is well-mixed in the tank, and subsequently flows out of the tank at a rate of 2 gal/min. Let x(t) represent the amount of salt in lbs in the tank at time t, with t = 0) corresponding to the initial time. (a) Set up an IVP in terms of x and t modeling the problem described. You do not need to solve the IVP. (b) If the tank has a capacity of 5000 gal, and the system is allowed to run indefinitely so that the tank eventually overflows, what do you expect the amount of salt in the tank will be after a long time in this state? You do not need to solve the IVP to answer this question, but provide some brief explanation of your reas easoning. Problem 2. A tank initially contains 5 lb of salt dissolved in 1000 gal of water. A 2% brine solution (salty water) enters the tank at a rate of 3 gal/min, the resulting mixture is well-mixed in the tank, and subsequently flows out of the tank at a rate of 2 gal/min. Let x(t) represent the amount of salt in lbs in the tank at time t, with t = 0) corresponding to the initial time. (a) Set up an IVP in terms of x and t modeling the problem described. You do not need to solve the IVP. (b) If the tank has a capacity of 5000 gal, and the system is allowed to run indefinitely so that the tank eventually overflows, what do you expect the amount of salt in the tank will be after a long time in this state? You do not need to solve the IVP to answer this question, but provide some brief explanation of your reas easoning