Question

-2t A tank initially contains 10 liters of water and 5 grams of salt. Salt water containing 3+ e grams of salt per liter is pumped into the tank at a rate of 2 liters per minute. The solution of salt water is instantaneously, perfectly mixed and then pumped out at a rate of 2 liters per minute. Determine when, to three decimal places, the concentration of the salt leaving the tank is within 0.01 grams/liter of the salt entering the tank.

Answer 1

et rect) be the amount of salt at time to d = (3 + 62t) 2 - 2 (*) • x(0)=5 10 dx = 6+2e2t - ox at da tx = 6+212 at 5 Home genous soln m+ 0 me 45 Malt) = C, est xp I (6+20 2t om Dit +30 xalt) = 30 t = 2 +/ *pt = 30 - loent a(t) = Gets - lo ez xo) = c.-10 + 30 = 5 c - 10 + 270 =5 C = 5-260 G = -215 9

xH) = -215 45 10 ezt +30 3 =0.01 ces (34e-24) +255 +215 90 en 67 6-3 80 t = 27.38 minutes.