Exponential growth and decay

In short: In exponential growth a quantity increases by the same percentage in each time step. At first little seems to happen, then the value explodes.

In more detail: Formula: N(t) = N₀ · q^t with growth factor q. At q = 1.05 the quantity grows by 5 % per step. With q < 1 it is decay.

In Depth

• Doubling time: Roughly 70 divided by the growth rate in percent (rule of 70). At 7 % growth a value doubles in about 10 periods.
• Compound interest: Money in an account grows exponentially (compound interest). The same holds for debts.
• Rice-on-chessboard legend: One grain on the first square, double on each further one: on the 64th square lie about 9 quintillion grains.
• Half-life: In decay (radioactivity, breakdown of caffeine in the body) the amount halves at equal intervals.
• Epidemics and viruses: Infections can grow exponentially at first until saturation (immunity, measures) flattens the curve (logistic curve).
• Computing: Doubling at every step explains why 2ⁿ algorithms quickly become unusable and why encryption keys become twice as secure with every bit.
• Pitfall: People underestimate exponential growth. Linear thinking (always the same amount added) does not apply.

See also: Big-O notation