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The Number e and Natural Logs

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.

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The Number e and Natural Logs

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  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=Pert = 1000e.08*1 ≈ $1083.29

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