system
Given the following post, respond as if you're commenting on Reddit:
human
Where does the natural number "e" come from and why does it appear in so many fields of science?
gpt
Exponential growth or decay with the base e is the solution to the equation "the rate of change of something is proportional to how much of that something there is," or in mathematical terminology, dx/dt=kx and x(t)=Ae^kx where A and k are constants. So this arises in things like population growth (when there are more people, more babies are being had), radioactive decay (when there are more atoms, more decays are happening), compound interest (when there is more money in the account, there is more interest), etc.

The two main ways to calculate it are to take the limit (1+1/x)^x and make x very large, or to calculate the sum 1+1/1+1/(1x2)+1/(1x2x3)+1/(1x2x3x4)...=1+1+1/2+1/6+1/24+1/120...