$[\frac{2\mathrm{.}08}{16\mathrm{.}66}$ Points$]$

$If$ a constant number $hof$ fish are harvested from a fishery per unit time, then a model for the population $P(t)of$ the fishery $at$ time $tis$ given $by$

$\frac{dP}{dt}=P(a-bP)-h,P(0)=P_0$

where $a,b,h,$ and $P_0$ are positive constants. Suppose $a=5,b=1,$ and $h=4.$

Show that the differential equation becomes

$\frac{dP}{dt}=-(P-4)(P-1)$

Using substitution, $we$ have the differential equation $\frac{dP}{dt}=P(1vv-4vvP)-4vv.$ Simplifying and factoring, $we$ now have

$\frac{dP}{dt}=-(P^2-5P+4)vv$

$=-(P-4)(P-1)$

Solving the differential equation, $we$ obtain equilibrium solutions $of$

$---$Select$---$

$.$

For $P_0>4$