. As shown in Figure 8.2.6 two large connected mixing tanks A and B initially contain 100 gallons of brine. Liquid is pumped in and out of the tanks as indicated in the figure; the mixture pumped...

Solve the exercise in the image, by using differential equations, solve the 3 sections, that is, a, b and c, without omitting any step to arrive at the result.

Extracted text: . As shown in Figure 8.2.6 two large connected mixing tanks A and B initially contain 100 gallons of brine. Liquid is pumped in and out of the tanks as indicated in the figure; the mixture pumped between and out of a tank is assumed to be well-stirred. Figure 8.2.6 Mixing tanks pure water mixture 2 gal/min 1 gal/min A B mixture 1 gal/min mixture mixture 2 gal/min 1 gal/min (a) Construct a mathematical model in the form of a linear system of first- order differential equations for the number of pounds ¤1(t) and x2 (t) of salt in tanks A and B, respectively, at time t. Write the system in matrix form. (b) Use the eigenvalue method of this section to solve the linear system in part (a) subject to ¤1 (0) = 20, æ2 (0) = 5. (c) Use a graphing utility or CAS to plot the graphs of ¤1 (t) and #2(t) in the same coordinate plane.