Suppose we have 3 tanks, A, B, and C that hold 200, 150, and 100 galons of brine, respectively. Also, suppose that the system is closed, and further that the liquid (which is well-stirred) is pumped between the tanks only.
Tank A is connected to B, and tank B is connected to C. Tank C is connected to A.
Mixture of 4 gal/min goes from tank A to tank B.
Mixture of 4 gal/min goes from tank B to tank C.
Mixture of 4 gal/min goes from tank C to tank A.
(So the flow goes A -> B -> C -> A)
1.) Construact a model for the number of pounds of salt x_1(t), x_2(t), x_3(t) at time t in the tanks A, B, C (respectively).
2.) From #1, write a system in the form X' = AX.