13. 14. Mixing problem 2. A tank with a capacity of dill] L is full of a mixture of water and chlorine with a conceutration of OHS g of chlorine per 1 L. In order to reduce the conceutration of chlorine. fresh water is pumped into the timk at a rate of Li L} s. The mixture is kept stirred :md is pumped out at a rate of 8 Lfs. {a} Model the above problem as an IUP with a separable DDE. {h} Find the amount of chlorine in the tank as a fuuctiou of time. {c} How much chlorine is in the tank after 1 miuute? Logistic Model. A populatiou P as a function of time t can he model by ODE. In a natural growth case without limited resources. % = RF for some growth constant it. However. iu reality au environmeut has limited resources Emd carries some carrying capacity;r 411'. the maximum population that it is capable of sustaining. The logistic differential equation incorporates these two ideas as follows: $=kP(l%). {4) Assume 5.: aud M' are constants and Plj = P". solve the logistic HIDE. You may refer #3114 for the details