i know a logarithm is the inverse of exponents… but i just cannot fathom how these are supposed to work in calculus, why we’re deriving them, what “e” means, why it’s important etc.
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for reference currently taking calculus ab as well
In: Mathematics
e is the value that ties in with growth where the rate of growth at a given is proportional to the current size and occurs continually, rather than incrementally.
This is represented by e^x
The rate of growth/slope of the curve is equal to the value of the curve at any location, and the area under the curve between 0 and any location is equal to the value of the curve at that location.
Ie: the growth is equal to the population
This can be manipulated with constants ie e^kx for other growth rates, but in general anything with continuous growth is going to have an equation involving e
ln is the log in base e
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