$1.(4$ marks$)$ Scientists are observing herds of squirbos as they move into new territory on the Nretsew island. Based on past migrations into new land, the scientists have come up with the following model for $\backslash ($ N$($t$)\backslash )($the population of the herd over time$)$: $\backslash [\backslash$frac$\{\backslash$mathrm$\{$d$\}$ N$\}\{\backslash$mathrm$\{$~d$\}$ t$\}=-$N$\backslash$left$(1-\backslash$frac$\{$N$\}\{20\}\backslash$right$)\backslash$left$(1-\backslash$frac$\{$N$\}\{500\}\backslash$right$)\backslash ]$ In this question we're going to analyze the population of squirbos from the differential equation without solving it$.$ Indeed solving it is not something we've taught in this course, so solving it would require material beyond the course which will be considered cheating. $($a$)(1$ mark$)$ Sketch a phase$-$plot for this autonomous differential equation. $($b$)(2$ mark$)$ Identify each of the equilibrium states for the growth model. Classify each as $($asymptotically$)$ stable, $($asymptotically$)$ semistable, or $($asymptotically$)$ unstable. $($c$)(1$ mark$)$ By drawing an analogy to what you know about the logistic growth model, what is the carrying capacity for the new territory, according to the scientist's model? $($d$)(2$ marks$)$ Suppose a population of squirbos enters the land with a population less than $20$ members. What would you expect to happen to this population? What if the initial population was slightly greater than $20?$ State a real$-$world justification for this divide?