GOMPERTZ FUNCTION Meaning and
Definition
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The Gompertz function is a mathematical function that describes the sigmoidal growth or decay of a population, commonly used in biology, demography, and epidemiology. It is named after the British mathematician Benjamin Gompertz, who introduced it in the early 19th century.
The Gompertz function is defined by the equation:
y(t) = A * exp(-exp(r * (M - t) + 1))
Where:
- y(t) represents the population size or any other measured variable at time t.
- A is the upper asymptote, representing the maximum value that y(t) can reach.
- r is the growth rate, determining the slope of the sigmoid curve.
- M is the time parameter representing the point of inflection, where the growth rate is maximum.
The Gompertz function is characterized by a rapid increase or decrease at the initial phase, followed by a slowing growth or decay rate over time. It is widely used to model natural phenomena such as population growth or decline, tumor growth, and disease spread. The function accurately describes exponential growth in the initial stages and approaches the maximum asymptote as time progresses.
Additionally, the Gompertz function has various applications in predicting and analyzing social, economic, and demographic trends. Its flexibility and ability to capture complex growth patterns make it a valuable tool in understanding and forecasting population dynamics.
Etymology of GOMPERTZ FUNCTION
The term "Gompertz function" is named after Benjamin Gompertz, an English mathematician and actuary who introduced and studied the function in the early 19th century.
The word "function" itself derives from the Latin word "functio", meaning performance, execution, or discharge. It entered the English language in the late 16th century with the same meaning.
So, the term "Gompertz function" combines Gompertz's surname with the general mathematical term "function" to refer to the specific mathematical function introduced and studied by Benjamin Gompertz.
