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Sub-exponential growth. A common explanation for the growth of epidemics holds that 1 person infects 2, those 2 infect 4 and so on and so on with the number of infected doubling every generation. It is analogous to a game of tag where 1 person tags 2, those 2 tag 4 others who've never been tagged and so on. As this game progresses it becomes ...
Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 220 years, [1] although over the last century the scope of mathematical biology has greatly expanded. [citation needed] The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the ...
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. The ratio is called coefficient of proportionality (or proportionality constant) and its reciprocal is known as constant of normalization (or normalizing constant ). Two sequences ...
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]
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations N as the result of input size n for each function. In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated ...
The unsustainable exponential progression of a classic pyramid scheme in which every member is required to recruit six new people. To sustain the scheme, the 2.2 billion people in the 12th layer would be required to recruit 13.1 billion more people for the 13th layer, even though there are not nearly enough people in the world to achieve that.
Exponential decay. A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant ( λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
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, . [1]
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