What is e (2.718…) and why does it literally appear everywhere?
In: 756
It’s a number that comes up when how fast something changes depends on how much of it there already is.
That sounds confusing, but it’s really easy to understand with some examples.
A bunch of rabbits live in the meadow. They do the rabbit thing, and soon enough there are more rabbits.
Now that there are more rabbits, that means more pairs of rabbit parents, which means they reproduce even faster! Which makes more rabbits, which leads to faster reproduction, which makes more rabbits… etc.
As you see, how fast the rabbits reproduce depends on how many rabbits there are. And when they reproduce, it creates more rabbits, which continues the loop! (obviously, for simplicity, I’m not including all the rabbits who die or get eaten or the time it takes them to grow up)
The other common example is interest. You gain interest based on how much money you have. And once you gain interest, now you have more money! So you gain more interest, which gives you more money, which gives you more interest… etc.
It appears in nature, e.g. in the patterns of certain plants, because how fast the plant is able to grow depends on how big it is already. Lots of things in nature, as well as in human society, have this kind of relationship.
Basically, when you write out the equations representing this relationship, e is the number that comes out as the most basic number that, when you put it in the equation, causes the equation to grow at the same rate as its current size. Everything else is just multiplying this basic equation by some other numbers to change the exact rate and amount.
(for the pedants, yes, I should be saying “function” and not “equation”)
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