Hyperbolic growth

When a quantity grows towards a singularity under a finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth. More precisely, the reciprocal function ${\displaystyle 1/x}$ has a hyperbola as a graph, and has a singularity at 0, meaning that the limit as ${\displaystyle x\to 0}$ is infinite: any similar graph is said to exhibit hyperbolic growth.

If the output of a function is inversely proportional to its input, or inversely proportional to the difference from a given value ${\displaystyle x_{0}}$, the function will exhibit hyperbolic growth, with a singularity at ${\displaystyle x_{0}}$.

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