A function is called an exponential function if
When , is an increasing function
When , is a decreasing function
In either case, is a one-to-one function,
and has the horizontal asymptote .
The domain and the range of are given by
Property of one-to-one functions.
If is a one-to-one function,
with positive real value ,
Natural exponential function.
A function is called the natural exponential function if
is the number given by (1).
Exponential growth and decay.
Suppose that the value at time is expressed as
with initial value at time .
If , we say that the value ``increases exponentially''
and is often called the ``rate of growth.''
If , we say that the value ``decreases exponentially''
and is often called the ``rate of decay.''
Department of Mathematics
Last modified: 2005-09-29