Answer Happy

1. 20 pts. – Suppose we have a three-stage system (see the image below). The first brine tank has fresh water flowing into it while mixed brine flow from tank 1 into tank 2, from tank 2 to tank 3, and then out of tank 3. Let xi(t) represent the amount of salt (in pounds) in tank i at time t. The system of equations for this system is provided below. Solve the system and plot the salt concentration in each tank as a function of time (from t=0.1 to t=30 minutes). lbs. gal/ 1 rate of salt loss (gal/min) min) min xi(t) =-1(9 in)(gal)xi(lbs. of salt) =- kıxı v (mah)(ga) (lbs. of salt) = gal 1 )V - r ki = VE V1,2,3 = 20,40,50 xi(t)=-k1X1 xu(t) = k1X1 – k2x2 X1,2,3(0) = 15,0,0 x's(t) = k2X2 – k3x3 = (gal r= 101 min