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Logarithmic growth. In mathematics, logarithmic growth describes a phenomenon whose size or cost can be described as a logarithm function of some input. e.g. y = C log ( x ). Any logarithm base can be used, since one can be converted to another by multiplying by a fixed constant. [1] Logarithmic growth is the inverse of exponential growth and ...
Hyperbolic growth. The reciprocal function, exhibiting hyperbolic growth. When a quantity grows towards a singularity under a finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth. [1] More precisely, the reciprocal function has a hyperbola as a graph, and has a singularity at 0, meaning that the limit as is ...
The stretched exponential function. is obtained by inserting a fractional power law into the exponential function. In most applications, it is meaningful only for arguments t between 0 and +∞. With β = 1, the usual exponential function is recovered. With a stretching exponent β between 0 and 1, the graph of log f versus t is ...
To the right is the long tail, and to the left are the few that dominate (also known as the 80–20 rule ). In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to a power of the change, independent of the initial ...
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 ...
Bacterial growth. Growth is shown as L = log (numbers) where numbers is the number of colony forming units per ml, versus T (time.) Bacterial growth is proliferation of bacterium into two daughter cells, in a process called binary fission. Providing no mutation event occurs, the resulting daughter cells are genetically identical to the original ...
Logistic function. A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation. where. is the carrying capacity, the supremum of the values of the function; is the logistic growth rate, the steepness of the curve; and. is the value of the function's midpoint. [1]
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 ...