Difference between revisions of "Logistic growth and decay models"
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| + | [[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 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. | ||
| + | |||
| + | For values of <math>x</math> in the domain of real numbers 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://openstax.org/books/calculus-volume-2/pages/4-4-the-logistic-equation The Logistic Equation], OpenStax Calculus Volume 2 | ||
* [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. | ||
| + | |||
| + | == Licensing == | ||
| + | Content obtained and/or adapted from: | ||
| + | * [https://en.wikipedia.org/wiki/Logistic_function Logistic function, Wikipedia] under a CC BY-SA license | ||
Latest revision as of 17:24, 28 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.
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
- The Logistic Equation, OpenStax Calculus Volume 2
- 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.
Licensing
Content obtained and/or adapted from:
- Logistic function, Wikipedia under a CC BY-SA license
