# "What are the practical uses of e? How can e be used for practical mathematics? This is for a presentation on (among other numbers) e, aimed at people between the ages of 10 and 15. To clarify what I want: Not wanted: e^(i pi)+1=0 is cool, but (as far as I know) it can't be used for practical applications outside a classroom. What I do want: e I think is used in calculations regarding compound interest. I'd like a simple explanation of how it is used (or links to simple explanations), and more examples like this."

Antwan Perez 2022-10-21 Answered
What are the practical uses of e ?
How can e be used for practical mathematics? This is for a presentation on (among other numbers) e, aimed at people between the ages of 10 and 15.
To clarify what I want:
Not wanted: ${e}^{i\pi }+1=0$ is cool, but (as far as I know) it can't be used for practical applications outside a classroom.
What I do want: e I think is used in calculations regarding compound interest. I'd like a simple explanation of how it is used (or links to simple explanations), and more examples like this.
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Zackary Mack
$\frac{1}{e}=\underset{n\to \mathrm{\infty }}{lim}{\left(1-\frac{1}{n}\right)}^{n}$
So, it appears in a large amount of games, for example, consider a game with n players, where each player has $\frac{1}{n}$ (independent) chances of win. When n growth, the probability that there is no winner is (very quickly) close to $\frac{1}{e}$
It stays true, even for some cases where it is not independent. Play the game with n balls (with numbers from 1 to n, one on each ball), and n players (each player has a different number). Then each player draws a ball in the bag (he can't see which ball he draws, and he keeps it). Once again, the chance of no one draws his own number is close to $\frac{1}{e}$ (for enough large n, a class of 15 children is enough)...
If, in such experiment, you make a redraw until there is no winner, the average number of draws needed is e.