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　　External Websites Ask the Chatbot a Question Written by L. Sue Baugh L. Sue Baugh is a writer and editor who works in the educational, business, and science/medical fields. L. Sue Baugh Fact-checked by The Editors of Encyclopaedia Britannica Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree. They write new content and verify and edit content received from contributors. The Editors of Encyclopaedia Britannica Last Updated: Jan 2, 2025 • Article History Table of Contents Table of Contents Ask the Chatbot a Question { "@context": "https://schema.org", "@type": "FAQPage", "mainEntity": [ { "@type" : "Question", "name" : " What is the logistic function used for? ", "acceptedAnswer" : { "@type" : "Answer", "text" : "The logistic function describes growth rates of quantities, such as populations, over time. It is used in such fields as biology, sociology, agriculture, and economics." } } , { "@type" : "Question", "name" : " Who developed the logistic function? ", "acceptedAnswer" : { "@type" : "Answer", "text" : "Belgian mathematician Pierre-Franu00E7ois Verhulst developed the logistic function." } } , { "@type" : "Question", "name" : " What does the logistic function equation represent? ", "acceptedAnswer" : { "@type" : "Answer", "text" : "The equation represents a quantity that changes with timeu2014with parameters for growth rate, initial value, and maximum valueu2014forming an S-shaped curve." } } , { "@type" : "Question", "name" : " What are the three stages of the logistic function curve? ", "acceptedAnswer" : { "@type" : "Answer", "text" : "The stages are (1) initial slow-to-rapid growth, (2) midpoint inflection from positive to negative curvature, and (3) leveling off toward maximum value." } } ] } Top Questions What is the logistic function used for? The logistic function describes growth rates of quantities, such as populations, over time. It is used in such fields as biology, sociology, agriculture, and economics.

　　Who developed the logistic function? Belgian mathematician Pierre-François Verhulst developed the logistic function.

　　What does the logistic function equation represent? The equation represents a quantity that changes with time—with parameters for growth rate, initial value, and maximum value—forming an S-shaped curve.

　　What are the three stages of the logistic function curve? The stages are (1) initial slow-to-rapid growth, (2) midpoint inflection from positive to negative curvature, and (3) leveling off toward maximum value.

　　logistic function, an equation describing growth rates of quantities, such as populations, over time and graphed as an S-shaped, or sigmoid, curve. The equation is applied in many fields, such as biology, sociology, agriculture, and economics. The logistic function is writtenP(t) = P0/1 + P0(ert − 1)/K,where the function P(t) is the quantity that changes with time t; r is the quantity’s growth (or decay) rate, represented by the slope of the S-shaped graph; e is the base of the exponential function; P0 is the initial value of the quantity; and K is the maximum or saturation ...(100 of 592 words)

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