Exponential growth and the rule of 72 · Pulse Beat
Something grows exponentially when it increases by the same percentage each period, not the same amount. Money earning compound interest does this.
Something grows exponentially when it increases by the same percentage each period, not the same amount. Money earning compound interest does this.
Start with 100 and add 10% each year: 110, 121, 133.1, 146.4... After n years you have 100 × 1.1ⁿ.
A quick estimate for how long it takes to double is the rule of 72: divide 72 by the percentage. At 8% growth, 72 / 8 = 9 years. At 2%, 36 years.
The same maths describes anything that multiplies: bacteria, a viral post, an epidemic early on. The reverse, shrinking by a fixed percentage each period, is exponential decay, and it describes radioactive half-life.
Exponential growth feels slow at first and then sudden. Doubling a grain of rice 63 times across a chessboard gives more than nine quintillion grains on the last square.