## 2nd Midterm

## Fall 2001

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