what is the purpose of the value e?
In: Mathematics
The mathematical constant e is referred to as representing natural growth. Unlike other popular constants like pi, e does not have a handy visual to explain it. Instead it can be thought of using banks and interest:
(For true ELI5, interest means “the bank will add ‘this much’ to your money at the specified time)
If we have a bank that generously offers 100% interest every year, and you give them $1, then after a year you will have $2.
But wait! A rival bank wants to offer 50% interest TWICE a year if you bank with them. At first, you may think that 50% twice = 100% once, but that isn’t the case. After 6 months with this bank, your total + interest will be $1.50. Then another 6 months later it would be $2.25, getting $0.75 from 50% of the $1.50.
So it would seem that even if the % interest adds to the same 100%, getting it more often leads to giving you more money! So what about a bank that offers 25% interest every 3 months? Or 8.3% every month? How about an inconceivablely small percentage interest at every fraction of a millisecond throughout the year?
You’ll find that the final amount tends toward the value of e if you were able to gain interest at a “natural” rate of growth.
100% once a year: $2
50% twice a year: $2.25
25% four times a year: $2.4414
8.3% twelve times a year: $2.613035
Every possible moment in a year: $2.71828 (approaching the value of e)
e is also important in Calculus and the natural log, but those are waaaay beyond a 5 year old.
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