= The flow system shown in the figure is activated at time t 0. Let Qi(t) denote the amount of solute present in the ith tank at time t. Assume that all the flow rates are a constant 10 L/min. It follows that the volume of solution in each tank remains constant; assume this volume to be 1000 L. The concentration of solute in the inflow to Tank 1 (from a source other than Tank 2) is 0.6 kg/L, and the concentration of solute in the inflow to Tank 2 (from a source other than Tank 1) is 0 kg/L. Assume each tank is mixed perfectly. a. Set up a system of first-order differential equations that models this situation. 2-882-8 b. If Q1(0) = 20 kg and Q2(0) = 10 kg, find the amount of solute in each tank after t minutes. Q1(t) = Q2(t) = kg kg Tank 1 Tank 2 (Hint: You need to find the general homogeneous solution and also guess a particular solution, just as we did for single equations. Try guessing x(t) where C and D are constants.) = [២]. c. As t∞, how much solute is in each tank? In the long run, Tank 1 will have kg of solute. In the long run, Tank 2 will have kg of solute. (Reread the question and think about why this answer makes sense.)

The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.

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