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Growth Rate (biology)
Growth rate may refer to: By rate *Asymptotic analysis, a branch of mathematics concerned with the analysis of growth rates *Linear growth *Exponential growth, a growth rate classification *Any of a variety of growth rates classified by such things as the Landau notation By type of growing medium *Economic growth, the increase in value of the goods and services produced by an economy *Compound annual growth rate Compound annual growth rate (CAGR) is a business, economics and investing term representing the mean annualized growth rate for compounding values over a given time period. CAGR smoothes the effect of volatility of periodic values that can render ... 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 In biology *The rate of growth in any biological system, see Growth § Biology. {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotic Analysis
In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing Limit (mathematics), limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as becomes very large, the term becomes insignificant compared to . The function is said to be "''asymptotically equivalent'' to , as ". This is often written symbolically as , which is read as " is asymptotic to ". An example of an important asymptotic result is the prime number theorem. Let denote the prime-counting function (which is not directly related to the constant pi), i.e. is the number of prime numbers that are less than or equal to . Then the theorem states that \pi(x)\sim\frac. Asymptotic analysis is commonly used in computer science as part of the analysis of algorithms and is often expressed there in terms of big O notation. Definition Formally, given functions and , we define a binary relation f( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Growth
In mathematics, the term linear function refers to two distinct but related notions: * In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. For distinguishing such a linear function from the other concept, the term ''affine function'' is often used. * In linear algebra, mathematical analysis, and functional analysis, a linear function is a linear map. As a polynomial function In calculus, analytic geometry and related areas, a linear function is a polynomial of degree one or less, including the zero polynomial (the latter not being considered to have degree zero). When the function is of only one variable, it is of the form :f(x)=ax+b, where and are constants, often real numbers. The graph of such a function of one variable is a nonvertical line. is frequently referred to as the slope of the line, and as the intercept. If ''a > 0'' then the gradient is positive and th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Growth
Exponential growth occurs when a quantity grows as an exponential function of time. The quantity grows at a rate directly proportional to its present size. For example, when it is 3 times as big as it is now, it will be growing 3 times as fast as it is now. In more technical language, its instantaneous rate of change (that is, the derivative) of a quantity with respect to an independent variable is proportional to the quantity itself. Often the independent variable is time. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth). Exponential growth is the inverse of logarithmic growth. Not all cases of growth at an always increasing rate are instances of exponential growth. For example the function f(x) = x^3 grows at an ever increasing rate, but is much slower than growing exponentially. For example, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landau Notation
Big ''O'' notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by German mathematicians Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for ''Ordnung'', meaning the order of approximation. In computer science, big O notation is used to classify algorithms according to how their run time or space requirements grow as the input size grows. In analytic number theory, big O notation is often used to express a bound on the difference between an arithmetical function and a better understood approximation; one well-known example is the remainder term in the prime number theorem. Big O notation is also used in many other fields to provide similar estimates. Big O notation characterizes functions according to their growth rat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economic Growth
In economics, economic growth is an increase in the quantity and quality of the economic goods and Service (economics), services that a society Production (economics), produces. It can be measured as the increase in the inflation-adjusted Output (economics), output of an economy in a given year or over a period of time. The rate of growth is typically calculated as List of countries by real GDP growth rate, real gross domestic product (GDP) growth rate, List of countries by real GDP per capita growth, real GDP per capita growth rate or List of countries by GNI per capita growth, GNI per capita growth. The "rate" of economic growth refers to the Exponential growth, geometric annual rate of growth in GDP or GDP per capita between the first and the last year over a period of time. This growth rate represents the trend in the average level of GDP over the period, and ignores any fluctuations in the GDP around this trend. Growth is usually calculated in "real" value, which is real v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Annual Growth Rate
Compound annual growth rate (CAGR) is a business, economics and investing term representing the mean annualized growth rate for compounding values over a given time period. CAGR smoothes the effect of volatility of periodic values that can render arithmetic means less meaningful. It is particularly useful to compare growth rates of various data values, such as revenue growth of companies, or of economic values, over time. Equation For annual values, CAGR is defined as: :\mathrm(t_0,t_n) = \left( \frac \right)^\frac - 1 where V(t_0) is the initial value, V(t_n) is the end value, and t_n - t_0 is the number of years. CAGR can also be used to calculate mean annualized growth rates on quarterly or monthly values. The numerator of the exponent would be the value of 4 in the case of quarterly, and 12 in the case of monthly, with the denominator being the number of corresponding periods involved. In practice, CAGR calculations are often performed in Microsoft Excel. A convenient ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Growth Rate
Population growth is the increase in the number of people in a population or dispersed group. The global population has grown from 1 billion in 1800 to 8.2 billion in 2025. Actual global human population growth amounts to around 70 million annually, or 0.85% per year. As of 2024, The United Nations projects that global population will peak in the mid-2080s at around 10.3 billion. The UN's estimates have decreased strongly in recent years due to sharp declines in global birth rates. Others have challenged many recent population projections as having underestimated population growth. The world human population has been growing since the end of the Black Death, around the year 1350. A mix of technological advancement that improved agricultural productivity and sanitation and medical advancement that reduced mortality increased population growth. In some geographies, this has slowed through the process called the demographic transition, where many nations with high standards of liv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Growth Rate (group Theory)
In the mathematical subject of geometric group theory, the growth rate of a group with respect to a symmetric generating set describes how fast a group grows. Every element in the group can be written as a product of generators, and the growth rate counts the number of elements that can be written as a product of length ''n''. Definition Suppose ''G'' is a finitely generated group; and ''T'' is a finite ''symmetric'' set of generators (symmetric means that if x \in T then x^ \in T ). Any element x \in G can be expressed as a word in the ''T''-alphabet : x = a_1 \cdot a_2 \cdots a_k \text a_i\in T. Consider the subset of all elements of ''G'' that can be expressed by such a word of length ≤ ''n'' :B_n(G,T) = \. This set is just the closed ball of radius ''n'' in the word metric ''d'' on ''G'' with respect to the generating set ''T'': :B_n(G,T) = \. More geometrically, B_n(G,T) is the set of vertices in the Cayley graph with respect to ''T'' that are within dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
