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.