13 and 14

minutes. 13. Mixing problem 2. A tank with a capacity of 400 L is full of a mixture of water and chlorine with a concentration of 0.05 g of chlorine per 1 L. In order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 4 L/s. The mixture is kept stirred and is pumped out at a rate of 8 L/s. (a) Model the above problem as an IVP with a separable ODE. (b) Find the amount of chlorine in the tank as a function of time. MTH 200 ODE: Separable and First-order Linear - Page 3 of 3 HW 09 (e) How much chlorine is in the tank after 1 minute? 14. Logistic Model. A population P as a function of time { can be model by ODE. In a natural growth case without limited resources. SP - kP for some growth constant k. However, in reality an environment has limited resources and carries some carrying capacity M, the maximum population that it is capable of sustaining. The logistic differential equation incorporates these two ideas as follows: Assume k and M are constants and P(0) - P. solve the logistic ODE. You may refer $9.4 for the details