Let $y(t)$ be a solution of $\dot{y} = \frac{1}{3} y (1 - \frac{y}{3})$ such that $y(0) = 6$. Determine $\displaystyle \lim_{t \to \infty} y(t)$ without finding $y(t)$ explicitly.

$\displaystyle \lim_{t \to \infty} y(t)$ =