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).
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.
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).