Exponential Growth

A quantity changes by a constant proportion per equal interval, so successive absolute changes depend on a changing base.

Exponential growth adds a constant proportion of the current quantity during each equal interval. With a discrete growth rate r, a starting quantity A becomes A × (1 + r)^t after t periods. Constant additions produce linear growth; constant proportional additions compound because the base changes.

At 20 percent growth per period, 100 becomes about 249 after five periods, rather than 200. The exact doubling time is ln(2)/ln(1 + r) periods; for continuous growth A × e^(kt), it is ln(2)/k. Real processes can change rates or encounter constraints, so a calculated exponential path is a conditional projection rather than evidence that the assumed growth will continue.

When to use it

Useful for explicitly proportional growth or decay scenarios and for comparing them with linear change.

How it can help

Calculate compounded changes and threshold times, then check whether the growth mechanism can persist.