Inverse, Exponential, and Logarithmic Functions

exponential function  -  A function of the form f (x) = a ^x 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,

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

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,

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

With exponential decay, k is less than zero.