My name is Professor Brennock and today I am going to teach you about the letter “e.” The letter “e” is one of the more famous irrational numbers and is very important. The letter is often called Eulers Number and stands for the numeric value of 2.718. The number was first used by John Napier who used it with logarithms in the1600’s. It acts as a natural constant just like pi would.

The e constant is defined as the limit:

The value of e is also equal to 1 + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! + 1/6! + 1/7! + ... (etc)

As you can see by the graph, given the equation the larger number you substitute in for “n” the closer you get to the actual value of  “e”.

A few special things about “e” is that the derivative of e^x is special because it is equal to itself and it is the base for continuous, natural decay and growth

e is the base rate of growth shared by all continually growing processes. e lets you take a simple growth rate (where all change happens at the end of the year) and find the impact of compound, continuous growth, where every nanosecond (or faster) you are growing just a little bit.