Difference between revisions of "Logistic growth and decay models"
Jump to navigation
Jump to search
↑ Template:Cite journal
Rylee.taylor (talk | contribs) (fixing link to go straight to pdf) |
|||
| Line 1: | Line 1: | ||
| + | [[File:Logistic-curve.svg|thumb|320px|right|Standard logistic sigmoid function where <math>L=1,k=1,x_0=0</math>]] | ||
| + | |||
| + | A '''logistic function''' or '''logistic curve''' is a common S-shaped curve ([[sigmoid function|sigmoid curve]]) with equation | ||
| + | |||
| + | : <math>f(x) = \frac{L}{1 + e^{-k(x-x_0)}},</math> | ||
| + | |||
| + | where | ||
| + | : <math>x_0</math>, the <math>x</math> value of the sigmoid's midpoint; | ||
| + | : <math>L</math>, the curve's maximum value; | ||
| + | : <math>k</math>, the logistic growth rate or steepness of the curve.<ref name=verhulst1838>{{cite journal |first= Pierre-François |last=Verhulst |year= 1838 |title = Notice sur la loi que la population poursuit dans son accroissement |journal = Correspondance Mathématique et Physique |volume = 10 |pages = 113–121 |url = https://books.google.com/books?id=8GsEAAAAYAAJ |format = PDF |access-date = 3 December 2014}}</ref> | ||
| + | |||
| + | For values of <math>x</math> in the domain of [[real number]]s from <math>-\infty</math> to <math>+\infty</math>, the S-curve shown on the right is obtained, with the graph of <math>f</math> approaching <math>L</math> as <math>x</math> approaches <math>+\infty</math> and approaching zero as <math>x</math> approaches <math>-\infty</math>. | ||
| + | |||
| + | ==Resources== | ||
* [https://mathresearch.utsa.edu/wikiFiles/MAT1093/Exponential%20growth%20and%20decay%20models/Esparza%201093%20Notes%207.6.pdf Logistic growth and decay models]. Written notes created by Professor Esparza, UTSA. | * [https://mathresearch.utsa.edu/wikiFiles/MAT1093/Exponential%20growth%20and%20decay%20models/Esparza%201093%20Notes%207.6.pdf Logistic growth and decay models]. Written notes created by Professor Esparza, UTSA. | ||
* [https://mathresearch.utsa.edu/wikiFiles/MAT1093/Exponential%20growth%20and%20decay%20models/Esparza%201093%20Notes%207.6B.pdf Logistic growth and decay models Continued]. Written notes created by Professor Esparza, UTSA. | * [https://mathresearch.utsa.edu/wikiFiles/MAT1093/Exponential%20growth%20and%20decay%20models/Esparza%201093%20Notes%207.6B.pdf Logistic growth and decay models Continued]. Written notes created by Professor Esparza, UTSA. | ||
Revision as of 09:39, 10 October 2021
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation
where
- , the value of the sigmoid's midpoint;
- , the curve's maximum value;
- , the logistic growth rate or steepness of the curve.[1]
For values of in the domain of real numbers from to , the S-curve shown on the right is obtained, with the graph of approaching as approaches and approaching zero as approaches .
Resources
- Logistic growth and decay models. Written notes created by Professor Esparza, UTSA.
- Logistic growth and decay models Continued. Written notes created by Professor Esparza, UTSA.
