Logistic Models with Differential Equations Practice Test

A bacteria culture follows $\frac{dy}{dt}=ky\left(1-\frac{y}{5000}\right)$ with $k>0$. If $y(0)=6000$, what happens to $y$ as $t\to\infty$?

A lab culture satisfies $\frac{dy}{dt}=ky\left(1-\frac{y}{400}\right)$ with $k>0$. If $y=400$, what is $\frac{dy}{dt}$?