Po�et kr�l�k� $P$ v �ase $t$ je �e�en�m diferenci�ln� 
rovnice
$$
dP /dt = cP (120 - P) \quad, P(0)=30 \quad, P(1)=80 \quad.
$$
�e��me separac�
$$
\int c \, dt = \int \frac{dP}{p(120-P)} =
1/120 \int \Left(
\frac{1}{P} + \frac{1}{120 - P} \Right) dP
$$
Po �prav�
$$
ct + A = 1/120 \ln \Vert 
\frac{p}{120 - P}
\Vert \quad .$$
Dosad�me podm�nky pro $t=0$ a $t=1$ a dostaneme
$P(t)= 120 / (1 + 3\cdot 6^{-t})$.
Tedy $P(t) = 100$ pro $t\doteq 1.51$.
L�sk�� se toho jist� do�ije.

(podle [Eason], 15 / problem 13 )