For each of the following application problems, set up an initial value problem that would model the situation. you must then solve exactly one of the ivps for (b), (c), or (d), and answer the accompanying question. (a) a 400-gal tank is initially filled with brine (salt-water mixture) containing 50 lb of salt. brine containing 1 lb of salt per gallon enters the tank at the rate of 5 gal/s, and the well-mixed brine in the tank flows out at the same rate. find the amount (t) of salt in the tank at time t. (b) a 250-gal tank is initially filled with brine (salt-water mixture) containing 100 lb of salt. brine containing 3 lb of salt per gallon enters the tank at the rate of 7 gal/s, and the well- mixed brine in the tank flows out at the rate of 9 gal/s. find the amount (t) of salt in the tank after 1 minute.