Starting with an initial value of

$$P$(0)$equals$=1010,$

the population of a prairie dog community grows at a rate of

Pprime$($t$)$equals$=2020$minus$$StartFraction t Over $2$ EndFractiont$2$

$($in units of prairie$$ dogs$/$month$),$ for

$0$less than or equals$$tless than or equals$4040.$

a$.$ What is the population

$1313$

months$$ later?

b$.$ Find the population$$ P$($t$)$ for

$0$less than or equals$$tless than or equals$4040.$