exponential

In mathematics, descriptive of a function in which the variable quantity is an exponent (a number indicating the power to which another number or expression is raised).

Exponential functions and series involve the constant e = 2.71828.... . Scottish mathematician John Napier devised natural logarithms in 1614 with e as the base.

Exponential functions are basic mathematical functions, written as e^x or exp x. The expression e^x has five definitions, two of which are: (i) e^x is the solution of the differential equation dx/dt = x (x = 1 if t = 0); (ii) e^x is the limiting sum of the infinite series 1 + x + (x²/2!) + (x³/3!) + ... + (xⁿ/n!).

Exponential growth is not constant. It applies, for example, to population growth, where the population doubles in a short time period. A graph of population number against time is an exponential growth function and produces a curve that is characteristically rather flat at first but then shoots almost directly upwards.