Suppose that a population develops according to the logistic equationdPdt$=0\mathrm{.}05$P$0\mathrm{.}00006667$P$2,$where t is measured in weeks.

A logistic equation has two equilibrium solutions. The higher one is called the carrying capacity, since if P models a population, then the carrying capacity is the maximum sustainable population that the environment can support.

What is the carrying capacity?

help $($numbers$)$

Is the solution increasing or decreasing when P is between $0$ and the carriying capacity?

$?$increasing$$decreasing$$

Is the solution increasing or decreasing when P is greater than the carrying capacity?

$?$increasing$$decreasing$$