超難的數學Word Problem!!!!!!!! 請高手入

Justify the logistic differential equation as a model for population growth:

dP/dt = kP(1-P/M)

Use the logistic model to find the population P of fish in a lake at time t. Biologists first stocked the late with 400 fish and estimated the carrying capacity to be 10,000. Biologists returned in a year and found that the population had already tripled.