What is it about the number e that makes it so that taking log to the base e is called the natural logarithm?
In: Mathematics
The natural log tells you how long 100% **continuous*** growth takes. If you have like, cells that divide (everything doubles), that’s 100% growth. That’s what’s natural about this: it comes up a lot in things that grow.
Say you have a really good savings account that doubles every year, 100% continuous growth. You start with $1 in it. How long until you have $10? `ln(10) = 2.3 years`. And if I have one of these accounts, and I want to know how much my $3 will grow in 5 years, well that’s `3e^5 = $445`.
EDIT: * – see the convo… I should have clarified how I’m calculating interest. Math good, words bad.
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