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Exponential growth is a process that increases quantity over time at an ever-increasing rate. It occurs when the rate of change is proportional to the quantity itself. See examples, formula, and applications in biology, physics, economics, finance, and computer science.
Exponential decay is a process where a quantity decreases at a rate proportional to its current value. Learn the differential equation, the decay constant, the mean lifetime, the half-life, and the applications of exponential decay in physics, chemistry, biology, and more.
Doubling time is the time it takes for a population to double in size or value. Learn how to calculate it from the growth rate, and see examples of doubling times for various phenomena such as population, inflation, interest and tumours.
A power law is a functional relationship between two quantities that varies as a power of each other. Learn about the empirical examples, properties, and scientific interest in power laws, such as the Pareto distribution, fractals, and universality classes.
Malthus wrote that all life forms, including humans, have a propensity to exponential population growth when resources are abundant but that actual growth is limited by available resources: "Through the animal and vegetable kingdoms, nature has scattered the seeds of life abroad with the most profuse and liberal hand. ...
The rule of 69.3 is a method for estimating how long it takes for an investment to double in value at a given interest rate. It is more accurate than the rule of 72 for continuous compounding, and can also be used for decay and inflation calculations.
The time constant, denoted by τ, is a parameter that characterizes the response of a first-order, linear time-invariant system to a step input. Learn how to calculate the time constant, its relation to the bandwidth, and its applications in physics, engineering and radioactive decay.
A geometric progression is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. Learn about its properties, sum, product, history and examples.