from where was the logarithmic constant pulled from?
In: Mathematics
I assume you mean “e” the exponential constant? It’s not pulled from somewhere, it naturally arises from a lot of exponential or logarithmic relationships.
Easy example is compound interest. If you invest $1 at a bank that pays 100% annual interest, how much you end up with depends on how frequently the bank pays out. The formula is “Total money = (1 + 1/n) ^ n” where “n” is how frequently you are paid. The more frequently you’re paid, the more money you end up with:
annual = (1 + 1/1) ^ 1 = $2
biannual = (1 + 1/2) ^ 2 = $2.25
quarterly = (1 + 1/4) ^ 4 = $2.44
monthly = (1 + 1/12) ^ 12 = $2.61
weekly = (1 + 1/52) ^ 52 = $2.69
daily = (1 + 1/365) ^ 365 = $2.71
…
and so on. If you keep shrinking the time between payments until the gap is infinitesimally small (e.g. take the limit), you will get $2.71828…. which is “e.”
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