1. The Number e and Natural Logs Chapter 8.4 and 8.3

2. The Number e Like π and i, e denotes a number. e, the Eular Number, is named after the mathematician that discovered it, Leonhard Eular (1707 – 1783). e is also known as the Natural Base. The number e is irrational – its’ decimal representation does not terminate or follow a repeating pattern. e ≈ 2.18281828459045…

3. The Natural Logarithm The logarithm with the base e is called the natural logarithm. Most scientific calculators have keys to evaluate natural logarithms.

4. Using e in “real life” e can be found in the formula to calculate Compound Interest for accounts that build interest continuously. A = Amount P = Principal r = rate t = time

5. More Money, More Problems Ex. Continuously compounded interest You deposit $1000.00 into an account that pays 8% annual interest compounded continuously. What is the balance after 1 year? P = 1000, r =.08, and t = 1 A=Pe rt = 1000e.08*1 ≈ $1083.29