Exponential function
As a last topic in this section we have to discuss a special exponential function. Actually this is so special that for several people it is THE exponential function. Following it is,
f( x ) = e^{x}
where e = 2.718281828...... . Note the difference among f( x )= b ^{x} and f( x ) = e^{x} . In the primary case b is any number which is meets the limitation given above whereas e is a very specific number. Also note that e is not a terminating decimal.
This special exponential function is extremely important & arises obviously in several areas. As noted above, this function arises so frequently that several people will think of this function if you talk regarding exponential functions. Let's get a quick graph of this function.