An exponent is a number that gives the power to which a base is raised. For example, in 32 the base is 3 and the exponent is 2.


Exponential equation

An equation of the form a x = b where a and b are numbers. For example, if 3x = 81 we can solve for x by restating 81 = 9 × 9 = 3 × 3 × 3 × 3, and so x = 4. More difficult problems are solved using logarithms: e.g., if 4x = 15, then xloge4 = loge15. Therefore 1.386x = 2.7081 and x = 1.9535 (to 4 decimal places).


Exponential function

A function of the form f(x) = ax where x is positive and does not equal 1. In terms of differential calculus, f '(x) = axlogea f(x) = ax.


Exponential growth

Since the value of ax increases considerably with increases in x, the term exponential growth is used loosely in statistics to refer to the very rapid growth in number of a quantity over a period of time. More accurately, it refers to an increase which, if plotted against units of time, would approximate closely to an exponential curve (the plotting of an exponential function).