John Spacey, May 21, 2016 updated on September 21, 2017
Exponential growth and hyperbolic growth are often confused because they both feature ever increasing rates of growth or decline. The main difference between them is that exponential growth moves towards infinity with time. Hyperbolic growth becomes infinity at a point in time in a dramatic event known as a singularity.
Exponential growth is characterized by an ever increasing growth rate or rate of decline. It eventually starts moving very quickly but remains a function of time. In other words, it doesn't suddenly jump to infinity. For example, exponential growth can be seen in the growth of bacteria, economies and certain environmental pollutants.
Hyperbolic growth and decline are characterized by a sudden and complete breakout or breakdown that instantly reaches infinity. For example, a company with a high debt load based on floating rates may be marginally profitable at a 3% base rate, at 4% it may struggle but survive, at 5% it suddenly and dramatically fails.
Exponential vs Hyperbolic
Growth defined by an exponential function.
Growth that reaches a singularity at a finite point.