Set n higher to get better "natural base" estimates. The list shows each estimate from 1 to n using: (1 + 1/n)ⁿ which is continuous compounding. That yields this irrational number, the natural base, approximately 2.71828... when n is very large
The "natural base" is a constant in nature's continuous growth in bacteria, viruses, nuclear chain reactions, as well as decay, such as radioactive decay. For very high n, (1 + 1/n)ⁿ levels off at at about 2.71828... ("e" the natural base), by continuous compounding. if n=2 the estimation is (1 + 1/2)² = 2.25 if n=10 the estimation is (1 + 1/10)¹⁰ = 2.593742 if n approaches infinity, the number is e, 2.71828.. It's just as if you had 1 dollar that would earn 100% after a year, where n=1 means only 1 compounding period. If you had compounding twice a year, n=2, you'd get 50% increase after 6 months. Now make the compounding period every day of the year, n=365, then you get close to $2. 72. You don't get more than that increasing n to infinity, because it levels off at e, which is close to 2.72. e is usually called "Euler's number"
