If a function $f$ represents a system that varies in time, the existence of $\underset{t}{lim}f(t)$ means that the system reaches a steady state $($or equilibrium$).$ For the system of the population of a culture of tumor cells given by $p(t)=\frac{3800t}{t3},$ determine if a steady state exists and give the steady$-$state value.

For which of the following situations does there exist a steady state?

A$.\underset{t}{lim}f(t)$ does not exist and is neither $$ nor $-$

B$.\underset{t}{lim}f(t)=-$

C$.\underset{t}{lim}f(t)=k,$ where $k$ is a finite number