5. (Mixing Problem) A very large tank is initially filled with100 gallons of water containing 5 pounds of salt. Beginning at timet = 0, a brine solution with a concentration of 1 pound of salt pergallon flows into the top of the tank at 3 gallons per second, themixture is stirred, and the mixture flows out of the bottom of thetank at 2 gallons per second. (a) Letting w = pounds of salt in thetank at time t seconds, derive a differential equation using theprinciple dw dt = rate in ? rate out. (b) Find a formula for w interms of t by solving the differential equation in Part (a) afterfirst expressing it in the form P(t, w) dt + Q(t, w) dw =0
