Applications of the Number 'e'

Date: 02/21/2009 at 20:38:24
From: Googler
Subject: The number 'e'

I am doing an internet research project on the number 'e' and cannot
seem to find real-life examples of its usage.  I was wondering if you
could maybe give me a few real-life situations when a person would use
the number 'e' and why (I only need 3).  Thank you!

I have googled EVERYTHING and all the sites do is explain the number
'e' but do not give real-life examples.

Date: 02/22/2009 at 23:01:35
From: Doctor Minter
Subject: Re: The number 'e'

Hello,

Here are a few real-life examples that use the number "e."  Try to 
research these problems specifically, instead of searching for "e" 
itself, since, as you've noticed, this will only give you 
mathematical definitions.

  - Growth problems (especially population models)
  - Decay problems (radioactivity, for example)
  - Savings model (especially "continuous compounding interest")
  - Logistic model
  - Threshold model
  - Eigenvalue problems
  - Characteristic roots (it's more math, but at least it's 
    applied--see the following two items)
  - Charge on a capacitor (also RC-circuit or LRC-circuit)
  - Damping factor (or damping constant--this is the application of
    characteristic roots, used for oscillator problems such as LRC
    circuits or spring-mass problems)
  - Euler's formula (for complex numbers)
  - Newton's Law of Cooling/Heating (thermodynamics)
  - Plane waves (electrodynamics)
  - Boltzmann factor (thermodynamics)

I hope this helps.  Please feel free to write again if you need 
further assistance, or if you have any other questions.  Thanks for 
using Dr. Math!

- Doctor Minter, The Math Forum
  http://mathforum.org/dr.math/