Irrational number 'e'

Euler's number, "e", is one of the most important (if not the most important) fundamental constants in mathematics. It forms the base of the "natural" logarithm. It is an irrational number (meaning that it has no exact value, much like pi and can continue to be written forever), and while no one is exactly sure why, it is incredibly useful in describing a great many real-world phenomena, such as the continuous growth of compound interest and other exponential functions.

The mathematical constant e is the unique real number such that the value of the derivative (slope of the tangent line) of the function f(x) = e^x at the point x = 0 is equal to 1. The function e^x so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base e.

The number e is sometimes called Euler's number after the Swiss mathematician Leonhard Euler. (e is not to be confused with the Euler–Mascheroni constant, sometimes called simply Euler's constant.)The exponential function is one of the most important functions in mathematics. For a variable x, this function is written as exp(x) or e^x, where e is a mathematical constant, the base of the natural logarithm, which equals approximately 2.718281828, and is also known as Euler's number.

Also,The number e is irrational; it is not a ratio of integers. Furthermore, it is transcendental; it is not a root of any non-zero polynomial with rational coefficients. The numerical value of e truncated to 20 decimal places is e=2.718281828459045235360287471352662497757...

Some applications of the exponential function include modeling growth in populations, economic changes, fatigue of materials, and radioactive decay.
One of the original defining attributes of e, which is an interesting tidbit today, is the fact any bank account having a 100% APR interest rate which is compounded continuously, will grow at the exponential rate e^t, where t is time, discovered by Jacob Bernoulli. Intuitively, compounding an initial account of $1 would yield $e after one year.