The logistic equation for the population p (in thousands) at time t of certain species is given by dp/dt= p(2-p). Use the logistic equation to solve problems 1, 2 and 3 below.


a. If the initial population is 3000 (i.e. p(0) = 3), what is the limiting population as t approaches infinity. Explain.

b. Can a population of 1000 ever decline to 500?