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One equation used to analyze biological exponential growth uses the birth and death rates in a population. If, in a hypothetical population of size N, the birth rates (per capita) are represented as b and death rates (per capita) as d, then the increase or decrease in N during a time period t will be = ()
The model can also be written in the form of a differential equation: = with initial condition: P(0)= P 0. This model is often referred to as the exponential law. [5] It is widely regarded in the field of population ecology as the first principle of population dynamics, [6] with Malthus as the founder.
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 () = grows at an ever increasing rate, but is much slower than growing
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 the change raised to a constant exponent: one quantity varies as a power of another. The change is independent of the initial size of those quantities.
Since complex numbers can be raised to powers, tetration can be applied to bases of the form z = a + bi (where a and b are real). For example, in n z with z = i, tetration is achieved by using the principal branch of the natural logarithm; using Euler's formula we get the relation:
Kleiber's plot comparing body size to metabolic rate for a variety of species. [1]Kleiber's law, named after Max Kleiber for his biology work in the early 1930s, states, after many observations that, for a vast number of animals, an animal's Basal Metabolic Rate scales to the 3 ⁄ 4 power of the animal's mass.
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of ...
In mathematics, exponentiation, denoted b n, is an operation involving two numbers: the base, b, and the exponent or power, n. [1] When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: [1] = ⏟.