Problem $4$: $(3$ points, $1$ point each$)$

Suppose you're trying $to$ model a population $of$ bunnies. Initially

there are $100$ rabbits, and you notice that the growth rate $is0\mathrm{.}08$

bunnie$\frac{s}{d}ay.$ Moreover, due $tolimiting$ resources, $it$ seems that the

bunny population doesn't exceed $1000$ rabbits.

$(a)$ Set $up$ a differential equations model for the number $of$ rabbits

and follow the steps from lecture $to$ solve $it.$ You can skip the

partial fractions part $if$ you wish.

$(b)$ What $is$ the $limitof$ the solution $in(a)ast?$

$(c)$ For which $tdowe$ have $y(t)=900?$ Please find $an$ exact formula

for $t,as$ well $asan$ approximate value $(using$ your calculator$)$