Why is the number '$e$' so important? Why is it included in Pre-Calculus and Calculus?

Question

parthkohli · Answer

I mean there are like an infinite number of constants. Does anyone have an easy and a brief explanation of the uses of this constant and how it is obtained? Pi is significant as it is $C \over D$, but what is $e$ related to?

unklerhaukus · Answer

growth

unklerhaukus · Answer

and decay

parthkohli · Answer

How so?

aravindg · Answer

e^x is a function which grows faster than a polynomial function

parthkohli · Answer

Can you explain?

parthkohli · Answer

There are a lot of explanations of Euler's constant given on Wikipedia.

zarkon · Answer

http://en.wikipedia.org/wiki/E_(mathematical_constant)

unklerhaukus · Answer

$$e=\sum\limits_{k=0}^\infty\frac{1}{k!}$$

parthkohli · Answer

Yep. Was typing that ^ but what exactly is the significance?

zarkon · Answer

Euer's constant is this ... http://en.wikipedia.org/wiki/Euler%27s_constant

parthkohli · Answer

And how exactly is $e$ related to logarithms?

parthkohli · Answer

Oh @Zarkon I meant Euler's Number.

asnaseer · Answer

There was a very similar question asked here: http://math.stackexchange.com/questions/3319/why-is-the-number-e-so-important-in-mathematics Maybe that discussion can shed some light for you?

parthkohli · Answer

OH. NO WAY. No StackExchange. I am 12 years old. D:

asnaseer · Answer

:)

parthkohli · Answer

Hello sir, can you give me an explanation that is brief but not too brief? That'd be great! :)

asnaseer · Answer

This might be better for you then: http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/

parthkohli · Answer

Gotcha! Let me read the article, and I'd be back.

parthkohli · Answer

So $e = (1.01)^{100}$?

asnaseer · Answer

thats an approximation

parthkohli · Answer

Oh I see, so it is just related to exponential growth..

parthkohli · Answer

Okay! :) thank you

parthkohli · Answer

Wait a minute, so 100% rate of change is always e times the original value??

asnaseer · Answer

its actually defined as:$$e=\lim_{n\rightarrow\infty}(1+\frac{1}{n})^n$$

asnaseer · Answer

so you gave an example of n=100

asnaseer · Answer

which gives a very close approximation to e - sorry for misleading you earlier

unklerhaukus · Answer

how can i construct e on a number line/?

asnaseer · Answer

it's impossible since e is a transcendental number

asnaseer · Answer

see here for an explanation of this: http://mathandmultimedia.com/2010/10/25/irrational-numbers-on-the-number-line/

unklerhaukus · Answer

bother

asnaseer · Answer

don't tell it was your life long ambition to construct e on the number line :)

asnaseer · Answer

*don't tell me it...