# The Natural Base: e

### A short and simple lesson about e!

## Objectives

- What is e?
- When do I use e?
- Where did e derived from?
- What shape does f(x)=e^x look like

## When do I use e?

*It can be applied to*

*e*is a convenient way to model exponential growth and decay.__compound interest__and

__sum of the infinite series__(Taylor Series).

(The equation above is

**continuous compounding**.) (The equation above is

**the sum of infinite series.**)## Where did e derive from?

*e *is the value of the derivative of the function:

**f(x)= e^x **at the point x=0 is equal to 1.

This equation is called the** natural exponential function**.

(The picture above is a graph of

**natural exponential function**).## The most important things to remember!

*e*is called the**natural base**- f(x)=
*e*^x is called the**natural exponential function** *e*is derived from the natural exponential function*e*is used in applications involving growth and decay (e.g. continuous compound)- The graph of f(x)= e^x looks like a J