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In finance, the rule of 72, the rule of 70[1] and the rule of 69.3 are methods for estimating an investment 's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate number of periods required for doubling. Although scientific calculators and spreadsheet programs have ...
The doubling time is the time it takes for a population to double in size/value. It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things that tend to grow over time. When the relative growth rate (not the absolute growth rate) is constant ...
Exponential growth is a process that increases quantity over time at an ever-increasing rate. 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. Described as a function, a quantity undergoing exponential growth is an exponential function of time ...
Feigenbaum constants. Feigenbaum constant δ expresses the limit of the ratio of distances between consecutive bifurcation diagram on Li /Li + 1. In mathematics, specifically bifurcation theory, the Feigenbaum constants / ˈfaɪɡənˌbaʊm / [1] are two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map.
Period-doubling bifurcation. In dynamical systems theory, a period-doubling bifurcation occurs when a slight change in a system's parameters causes a new periodic trajectory to emerge from an existing periodic trajectory—the new one having double the period of the original. With the doubled period, it takes twice as long (or, in a discrete ...
The doubling time (t d) of a population is the time required for the population to grow to twice its size. [24] We can calculate the doubling time of a geometric population using the equation: N t = λ t N 0 by exploiting our knowledge of the fact that the population (N) is twice its size (2N) after the doubling time. [20]
This formulation has appealing properties such as no change being equal to zero, a 100% increase is equal to 1, and a 100% decrease is equal to −1. However, verbally referring to a doubling as a one-fold change and tripling as a two-fold change is counter-intuitive, and so this formulation is rarely used. Volcano plot showing metabolomic data ...
Bifurcation diagram. In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the system. [citation needed] It is usual to represent stable values with a solid line ...