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2. ### Exponential growth - Wikipedia

en.wikipedia.org/wiki/Exponential_growth

Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself.

3. ### Exponential decay - Wikipedia

en.wikipedia.org/wiki/Exponential_decay

Exponential decay is a scalar multiple of the exponential distribution (i.e. the individual lifetime of each object is exponentially distributed), which has a well-known expected value. We can compute it here using integration by parts . Decay by two or more processes [ edit] See also: Branching fraction

4. ### Biological exponential growth - Wikipedia

en.wikipedia.org/wiki/Biological_exponential_growth

Biological exponential growth is the unrestricted growth of a population of organisms, occurring when resources in its habitat are unlimited. Most commonly apparent in species that reproduce quickly and asexually, like bacteria, exponential growth is intuitive from the fact that each organism can divide and produce two copies of itself.

5. ### Doubling time - Wikipedia

en.wikipedia.org/wiki/Doubling_time

The equivalent concept to doubling time for a material undergoing a constant negative relative growth rate or exponential decay is the half-life . The equivalent concept in base- e is e -folding . Graphs comparing doubling times and half lives of exponential growths (bold lines) and decay (faint lines), and their 70/ t and 72/ t approximations.

6. ### Malthusian growth model - Wikipedia

en.wikipedia.org/wiki/Malthusian_growth_model

A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus, who wrote An Essay on the Principle of Population (1798), one of the earliest and most ...

7. ### Geometric progression - Wikipedia

en.wikipedia.org/wiki/Geometric_progression

greater than 1, there will be exponential growth towards positive or negative infinity (depending on the sign of the initial term). 1, the progression is a constant sequence. between −1 and 1 but not zero, there will be exponential decay towards zero (→ 0). −1, the absolute value of each term in the sequence is constant and terms alternate in sign.

8. ### Half-life - Wikipedia

en.wikipedia.org/wiki/Half-life

An exponential decay can be described by any of the following four equivalent formulas:  : 109–112 where N0 is the initial quantity of the substance that will decay (this quantity may be measured in grams, moles, number of atoms, etc.), N(t) is the quantity that still remains and has not yet decayed after a time t,