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Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent.
If the constant of proportionality is negative, then the quantity decreases over time, and is said to be undergoing exponential decay instead. In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay since the function values form a geometric progression.
The formula for exponential growth of a variable x at the growth rate r, as time t goes on in discrete intervals , is