$(1$ point$)$ A population P obeys the logistic model. It satisfies the equation

$($dP$)/($dt$)=(8)/(1300)$P$(13-$P$)$ for P$>0.$

$($a$)$ The population is increasing when

P$>$P$(0)=4$P$(55)$P$(55)=$

$($b$)$ The population is decreasing when P$>$

$($c$)$ Assume that P$(0)=4.$ Find P$(55).$

P$(55)=$