Many physical and biological systems involve time delays. A pure time delay has its output the same as its input but shifted in time. A more common type of delay is pooling delay. An example of such a feedback system is shown in Figure 5.3 Here the level of fluid in tank B determines the rate at which fluid enters tank A. Suppose this rate is given by R (t) = a[V-V(1)], where a and V are positive constants and V() is the volume of fluid in tank B at time t. (a) If the outflow rate R3 from tank B is constant and the flow rate R from tank A into B is R(t) = KV(1), where K is a positive constant and V (1) is the vol- ume of fluid in tank A at time t, then show that this feedback system is governed by the system dV dV = a(V-V(t)) - KV (t). = KV (1)-R. Pump Tank A V(1) R Tank B V(1) Power R3 Figure 5.3 Feedback system with pooling delay (b) Find a general solution for the system in part (a) when a = 5 (min)-, V = 20 L, K = 2 (min)-, and R3 = 10 L/min. (c) Using the general solution obtained in part (b), what can be said about the volume of fluid in each of the tanks as 1 +?