What is growth and how does it usually occur?
Since the question does not specify on what type of growth refers, the answer provided is about the population growth that usually is analyzed using statistical models.
For example, the exponential growth model is very accurate applied to the bacteria colonies where the population of colony increases in number at a constantly growing rate. The exponential growth models can be applied in bounded regions since unlimited growth cannot be a model for a real physical situation.
Other model of growth that occurs when the exponential growth reaches the level of saturation is called logistic growth. This logistic growth model can be applied to analyze the concentration of reactants and products in auto-catalytic reactions. It also can be applied to analyze the population growth.
Other model of growth is hyperbolic growth and this model can be successfully applied when the growth has one singularity in a finite time. In comparison with the exponential growth, that is finite, for finite time, the function that models the hyperbolic growth has an infinite limit at a finite time.