Assuming $P0,$ suppose that a population develops accoriling to the logistic eouation

$\frac{dP}{dt}=0\mathrm{.}02P-0\mathrm{.}0002P^2$

Where $f$ is measured in weeks. Answer the following queutions.

The carrying capacity is the limit$,$ lim $P(t)$ of the pepulation slae after a very long time. What is the carrying capacity?

Carrying Capacity a $$ growth rate". In this problem what is the value of $k?$

k $=$

$2.$ For ehat values of Pis the population increasing?

Answer fin $$ notationi: $$

$4.$ For what values of Pis the pobulation decreasing?

Answer in $$ foltation$)$: $$