The Natural Log & e

Put $1 in a bank that pays 100% interest, compounded every instant. You might expect $2 at the end of a year. You actually get $2.71828... — a mysterious, slightly-larger-than-2 amount. That number is e, and it appears because of compound interest's compounding-faster-as-you-slice-it effect. e is the natural base of growth: the one number where, miraculously, the rate of growth always equals the current amount. Nature uses e for everything continuous — population, radiation, cooling, charging capacitors. Its inverse is the natural logarithm, ln.