$\frac{dy}{dt}=\frac{(t^2-1)(y^2-2)}{y^2-4}$

Consider the population model

$\frac{dP}{dt}=0\mathrm{.}4P(1-\frac{P}{230})$

where $P(t)$ is the population at time $t.$

$($a$)$ For what values of $P$ is the population in equilibrium?

$($b$)$ For what values of $P$ is the population increasing?

$($c$)$ For what values of $P$ is the population decreasing?