Suppose that a tank initially contains 25 gallons of water with a concentration of 2 grams per gallon of salt. To gradually flush the salt out of the tank, you turn on a pipe which pours pure water into the tank at a rate of 5 gallons per hour. Suppose that a drain at the bottom of the tank opens 4. simultaneously, at which the well-stirred tank water leaves at a rate of 3 gallons per hour (a) Write down a differential equation which describes the amount X (t) of salt in the tank at any time t 2 0, together with an initial condition satisfied by Ax (b) By solving your DE and using the initial condition to find the undetermined constant, compute an exact formula for X(t). Use your formula to determine the number of days it will take for the amount of salt in the tank to fall under 1 gram. (Note that t is in units of hours in your equations.) You can take for granted that the tank is large enough to hold the increased volume of water