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Tetration is iterated exponentiation (call this right-associative operation ^), starting from the top right side of the expression with an instance a^a (call this value c). Exponentiating the next leftward a (call this the 'next base' b), is to work leftward after obtaining the new value b^c. Working to the left, consume the next a to the left ...
Definitions. For real non-zero values of x, the exponential integral Ei ( x) is defined as. The Risch algorithm shows that Ei is not an elementary function. The definition above can be used for positive values of x, but the integral has to be understood in terms of the Cauchy principal value due to the singularity of the integrand at zero. For ...
The doubling time is a characteristic unit (a natural unit of scale) for the exponential growth equation, and its converse for exponential decay is the half-life. As an example, Canada's net population growth was 2.7 percent in the year 2022, dividing 72 by 2.7 gives an approximate doubling time of about 27 years.
The von Bertalanffy growth function ( VBGF ), or von Bertalanffy curve, is a type of growth curve for a time series and is named after Ludwig von Bertalanffy. It is a special case of the generalised logistic function. The growth curve is used to model mean length from age in animals. [1] The function is commonly applied in ecology to model fish ...
In probability theory, a probability density function ( PDF ), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of ...
Quadratic growth. In mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position. "Quadratic growth" often means more generally "quadratic growth in the limit ", as the argument or sequence position goes to infinity – in big Theta notation ...
Exponential may refer to any of several mathematical topics related to exponentiation, including: Exponential function, also: Matrix exponential, the matrix analogue to the above. Exponential decay, decrease at a rate proportional to value. Exponential discounting, a specific form of the discount function, used in the analysis of choice over time.
Albert Allen Bartlett (March 21, 1923 – September 7, 2013) [2] was an American professor of physics at the University of Colorado at Boulder. As of July 2001 Professor Bartlett had lectured over 1,742 times since September, 1969 on Arithmetic, Population, and Energy. [3] [4] Bartlett regarded the word combination "sustainable growth" as an ...