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 3^x = 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 4^x = 15, then xlog_e4 = log_e15. Therefore 1.386x = 2.7081 and x = 1.9535 (to 4 decimal places).

 

Exponential function

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

 

Exponential growth

Since the value of a^x 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).