The Number "e"

Good Morning Class,

I am Professor Rhea and I will be teaching you all a little something about the number "e"

Now you might be wondering how the letter "e" can also be a number...this is possible because of the brilliant mind of Leonard Euler a Swiss mathematician. 

He found this using the following proof "(1+1/m)^m" and what this means is that as "m" reaches ∞ that (1+1/m)^m converges to "e" and when you plug m into the equation, the outcome stays at roughly 2.71

So "e" roughly equals 2.71

Or...

2.7182818284590452353602874713527 (and more ...) if you want to be exact!

Now because (1+1/m)^m approaches "e", any positive base "b" can be written as a power of "e" 

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

For example: (b = e^k) 

Because of this an exponential function f(t)=ab^t can be re-written in terms of "e" as f(t) = ae^kt

f(t) = ae^kt is used in Continous Compounding:

Where...
a = initial value
e = 2.71
k = the interest rate
t = the amount of time the interest rate is compounded over

That is it for our lecture today and if you have any questions you can visit me in my office hours or email me!

Have a good day,

Professor Rhea



Source: http://www.mathsisfun.com/numbers/e-eulers-number.html