EXPONENTIAL FUNCTION

in mathematics, a relation of the form y = ax, with the independent variable x ranging over the entire real line, as exponent (exp) of positive a. Probably the most important of the exponential functions is y = ex, sometimes written y = exp (x), in which e is the base of the natural system of logarithms. By definition x is a logarithm, and there is thus a logarithmic function the inverse of the exponential function (see the Figure). Specifically, if y = exp (x), then x = ln y, in which ln is a natural logarithm. The exponential function exp (x) is also defined as the sum of the series which converges for all x and in which n! is a product of the first n positive integers. Thus in particular, the constant The exponential functions are examples of so-called non-algebraic, or transcendental, functions. Others are the logarithmic functions and the hyperbolic functions. Exponential functions frequently arise and quantitatively describe a number of phenomena in physics.