Initial Conditions and Separation of Variables Practice Test

A population satisfies $\frac{dP}{dt}=\frac{1}{100}P(100-P)$ with $P(0)=20$. Which $P(t)$ is correct?

A bacteria culture satisfies $\frac{dP}{dt}=0.2P$ with $P(0)=50$. Which particular solution $P(t)$ fits?