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for some , < we say that G has a polynomial growth rate. The infimum k 0 {\displaystyle k_{0}} of such k' s is called the order of polynomial growth . According to Gromov's theorem , a group of polynomial growth is a virtually nilpotent group , i.e. it has a nilpotent subgroup of finite index .
However, we usually prefer to measure time in hours or minutes, and it is not difficult to change the units of time. For example, since 1 hour is 3 twenty-minute intervals, the population in one hour is S ( 3 ) = S 0 2 3 {\displaystyle S(3)=S_{0}2^{3}} .
r = the population growth rate, which Ronald Fisher called the Malthusian parameter of population growth in The Genetical Theory of Natural Selection, [2] and Alfred J. Lotka called the intrinsic rate of increase, [3] [4] t = time. The model can also be written in the form of a differential equation: =
The growth rate of a group is a well-defined notion from asymptotic analysis. To say that a finitely generated group has polynomial growth means the number of elements of length at most n (relative to a symmetric generating set) is bounded above by a polynomial function p(n). The order of growth is then the least degree of any such polynomial ...
Many pairs (b, τ) of a dimensionless non-negative number b and an amount of time τ (a physical quantity which can be expressed as the product of a number of units and a unit of time) represent the same growth rate, with τ proportional to log b. For any fixed b not equal to 1 (e.g. e or 2), the growth rate is given by the non-zero time τ.
Economic growth, the increase in value of the goods and services produced by an economy; Compound annual growth rate or CAGR, a measure of financial growth; Population growth rate, change in population over time; Growth rate (group theory), a property of a group in group theory
The equation for exponential mass growth rate in plant growth analysis is often expressed as: = Where: M(t) is the final mass of the plant at time (t). M 0 is the initial mass of the plant. RGR is the relative growth rate. RGR can then be written as:
Moreover, the function makes use of initial growth rate, which is commonly seen in populations of bacterial and cancer cells, which undergo the log phase and grow rapidly in numbers. Despite its popularity, the function initial rate of tumor growth is difficult to predetermine given the varying microcosms present with a patient, or varying ...