THE DOON SCHOOL

I.B. HL MATHS

n (1 + 1/n)^n

------------------

1 2

2 2.25

3 2.37

5 2.488

10 2.5937

100 2.7048

1,000 2.7169

10,000 2.71814

100,000 2.718268

1,000,000 2.7182804

...

The constant is base of the natural logarithm. is sometimes known as Napier's constant, although its symbol ( ) honors Euler.

Explain why e is important: It’s a fundamental constant, like pi, that shows up in growth rates.

Give an intuitive explanation: e lets you see the impact of any growth rate. Show how it’s used: ex lets you predict the impact of any growth rate and time period.

The first few digits are: 2.7182818284590452353602874713527 (and more ...)

It is often called Euler's number after Leonhard Euler. And Euler is spoken like "Oiler".

CalculatingThere are many ways of calculating the value of e, but none of them ever give an exact answer, because e is irrational (not the ratio of two integers).

But it is known to over 1 trillion digits of accuracy!

For example, the value of (1 + 1/n)n approaches e as n gets bigger and bigger:

n (1 + 1/n)n

1 2.00000

2 2.25000

5 2.48832

10 2.59374

100 2.70481

1,000 2.71692

10,000 2.71815

100,000 2.71827

QUESTIONS:

1. The number e is often called: (a) Euclid's number (b) Euler's number (c) Edison's number (d)Einstein's number

2. Which of the following is false?(a) The number e is irrational (b) The number e is transcendental (c) The number e is reald) The number e is imaginary

3. Which of the following has the least value?

(a) (b) (c) (d) e