1. In a logistic growth model, the rate at which a population grows is proportional to the number of individuals in the population and to how close the population is to the maximum carrying capacity of the environment. The logistic differential equation is
dP/dt = kP(M - P)
where M is the maximum carrying capacity for the environment, which is a constant, P is the number of individuals in the population and t is time. Solve this differential equation for P.
If M = 100,000, and k = .05 find the equation which satisfies the IVP P(0) = 20,000, and use this equation to predict P(10).
2. In the following improper integrals, if they converge, evaluate them. If they don't converge, state so.
3. Evaluate the following indeterminate forms