Consider two large mixing tanks shown in the figure below. Suppose tanks A initially contains 80 gallons of liquid and tank B initially contains 50 gallons of liquid. A liquid with a salt concentration of 3 lbs/gal is pumped into tank A. The well-stirred liquid is pumped in and out of the tanks as shown in the figure. Construct a system of first-order differential equations for the number of pounds of salt, x(t) and y(t), in tanks A and B at time t, respectively. Do not solve the system. Express your solution in the matrix/vector form X'(t) = AX(t) + F(t). How many pounds of salt will eventually be in tank B? %3D

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Differential Equations

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