Consider a three-tank mixing problem. Suppose tank 1 initially contains 10 lb of salt dissolved in 50 gal of water, tank 2 initially contains 5 lb of salt dissolved in 50 gal of water, and tank 3 initially contains 15 lb of salt dissolved in 50 gal of water. Starting at time t= 0, salt water with a concentration of 1/2 lb/gal flows into tank 1 at a rate of 20 gal/min, salt water with a concentration of 1/4 lb/gal flows into tank 2 at a rate of 20 gal/min, and fresh water flows into tank 3 at a rate of 20 gal/min. The well-stirred mixture flows from tank 1 to tank 2 at a rate of 10 gal/min and flows from tank 2 to tank 1 at a rate of 10 gal/min. The well-stirred mixture flows from tank 2 to tank 3 at a rate of 10 gal/min and flows from tank 3 to tank 2 at a rate of 10 gal/min. The well-stirred mixture flows out of tank 1 at a rate of 20 gal/min, out of tank 2 at a rate of 20 gal/min, and out of tank 3 at a rate of 20 gal/min. Let Qi(t) be the amount of salt in tank 1 after t minutes, Q2(t) be the amount of salt in tank 2 after t minutes, and Q3(t) be the amount of salt in tank 3 after t minutes. 1 Setup but DO NOT SOLVE an initial value problem for Q(t) (Q(t)] Q2(t) in the form |Q3(t) | Q' = AQ +b, Q(0) = Q. Consider a three-tank mixing problem. Suppose tank 1 initially contains 10 lb of salt dissolved in 50 gal of water, tank 2 initially contains 5 lb of salt dissolved in 50 gal of water, and tank 3 initially contains 15 lb of salt dissolved in 50 gal of water. Starting at time t= 0, salt water with a concentration of 1/2 lb/gal flows into tank 1 at a rate of 20 gal/min, salt water with a concentration of 1/4 lb/gal flows into tank 2 at a rate of 20 gal/min, and fresh water flows into tank 3 at a rate of 20 gal/min. The well-stirred mixture flows from tank 1 to tank 2 at a rate of 10 gal/min and flows from tank 2 to tank 1 at a rate of 10 gal/min. The well-stirred mixture flows from tank 2 to tank 3 at a rate of 10 gal/min and flows from tank 3 to tank 2 at a rate of 10 gal/min. The well-stirred mixture flows out of tank 1 at a rate of 20 gal/min, out of tank 2 at a rate of 20 gal/min, and out of tank 3 at a rate of 20 gal/min. Let Qi(t) be the amount of salt in tank 1 after t minutes, Q2(t) be the amount of salt in tank 2 after t minutes, and Q3(t) be the amount of salt in tank 3 after t minutes. 1 Setup but DO NOT SOLVE an initial value problem for Q(t) (Q(t)] Q2(t) in the form |Q3(t) | Q' = AQ +b, Q(0) =