The Number e and Natural Logs

Chapter 8.4 and 8.3

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…

The Natural Logarithm

• The logarithm with the base e is called the natural logarithm.

• Most scientific calculators have keys to evaluate natural logarithms.

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

More Money, More ProblemsEx. 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=Pert = 1000e.08*1 ≈ $1083.29