Suppose that a population develops according to the logistic equation dPdt$=0\mathrm{.}1$P$0\mathrm{.}0001$P$2$ where t is measured in weeks. $($a$)$ What is the carrying capacity? $($b$)$ Is the solution increasing or decreasing when P is between $0$ and the carrying capacity? $($c$)$ Is the solution increasing or decreasing when P is greater than the carrying capacity?