Exponential growth can be modeled as
$$ b (1+r)^N $$
For $b$ your starting quantity, $(1+r)$ your rate of growth, and $N$ the number of periods. But for $N \to \infty$, this formula can get out of control.
Is there a traditional way of controlling for this by factoring in some notion of a decay factor (so that for periods $N$ past some threshold, you stop growing asymptotically)?
The simplest extension of the exponential equation
$\frac{dx}{dt} = rx$
is the logistic equation
$\frac{dx}{dt} = rx(1-\frac{x}{C})$
where the rate of growth decreases as $x$ approaches $C$.
This differential equation has solution
$x(t)=\frac{Cx(0)e^{rt}}{C+x(0)(e^{rt}-1)}$
Interestingly, the discrete time step equivalent of the logistic equation (known as the logistic map) can exhibit chaotic behaviour.