An approximation for exponential.

[Alta]

Is there an approximation for exp(-k*L) with L large but finite??

 

[Hurkyl]

Well, what is

$$\lim_{L \to +\infty} e^{-kL}$$​

? Doesn't calculus tell you that limit would be a good approximation?

(P.S. are you making any assumptions about k? )

 

[Alta]

L is large but finite. No assumptions about k but it is positive.

 

[Delphi51]

Power series. Use as many terms as you like to improve accuracy.
I can't seem to do Latex code, but you'll find it here about a screenfull down.
http://en.wikipedia.org/wiki/Power_series

Oops - no good for negative exponent!

 

[Alta]

The trouble with that is that you can not say that exp(-k*L)=1+-k*L. you need the entire sum.