# Inverse, Exponential, and Logarithmic Functions

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#### Terms for Topic "Inverse, Exponential, and Logarithmic Functions"

exponential function  -  A function of the form f (x) = ax where a is any positive constant except 1.
inverse function  -  The inverse, f-1(x), reverses the operations of f (x). If f-1(x) exists for a certain function f, then f (f-1(x)) = x and f-1(f (x)) = x.
logarithmic differentiation  -  A method of finding the derivatives of functions that are raised to powers of the variable x. The use of logarithms helps to convert powers into products, which are more readily differentiated.
exponential growth  -  A type of growth in which the rate of change of the quantity is proportional to the quantity itself. In other words,

 = ky

Functions with this property have a constant percentage increase per time interval, and are of the form

 y = y0ekt

With exponential growth, k is greater than zero.
exponential decay  -  A type of decay in which the rate of change of the quantity is proportional to the quantity itself. In other words,

 = ky

Functions with this property have a constant percentage decrease per time interval, and are of the form

 y = y0ekt

With exponential decay, k is less than zero.