Match each scenario with the appropriate differential equation model. A tank contains 200 gallons of water in which 3 kilorams of salt is dissolved. A brine solution containing 0.4 kilograms of salt per gallon of water is pumped into the tank at a rate of 5 liters per minute, and the well stirred mixture is pumped out at the same rate. Let P(t) represent the amount of salt, P, at time t. A dP dt = 0.05P(1-700 = 7000P(1 + 0.05) B. dP dt Suppose that a population is growing according to a logistic model with carrying capcity 7000 and k = 0.5 per year. C. dp 2P = 2+ dt 200+ 3t A population of a small town grows in proportion to its current population. The initial population is 5000 and grows 4% per year. D. dp = 0.04P dt A tank contains 200 gallons of water in which 3 kilorams of salt is dissolved. A brine solution containing 0.4 kilograms of salt per gallon E. dp of water is pumped into the tank at a rate of 5 liters per minute, and the well stirred mixture is pumped out at a rate of 2 liters per minute. Let P(t) represent the amount of salt, P, at time t. 4P dt F. dP P = 5- dt 40 G. dp P = 2- dt 40 H. dP =0.04P(1- 2P = 2- 200 +3t =0.05P(1+ P 4P(1- 5000 2P 5- 200 + 3t 2P 2- 200-3t |08|09|08|09|08|6 dt 1. dp dt J. dp K. dp L dp dt dt dt M. dp dt = P 5000 P 70000