In mathematics, an exponential function is a function of the form in which the input variable x occurs as an exponent. A function of the form, where is a constant, is also considered an exponential function and can be rewritten as, with. As functions of a real variable, exponential functions are uniquely characterized by the fact that the growth rate of such a function is directly proportional to the value of the function. The constant of proportionality of this relationship is the natural logarithm of the base,
