MathLiveLogistic function
Gives the S-shaped curve that models growth which starts roughly exponentially and levels off at a maximum value. It is used in population biology, epidemiology, and machine learning to model saturating growth or to map real numbers into the interval between 0 and L.
f(x) = \frac{L}{1 + e^{-k(x-x_0)}}What the symbols mean
| value of the function at x | |
| independent variable, often time | |
| maximum value (supremum) of the curve | |
| logistic growth rate or steepness of the curve | |
| x-value of the midpoint, where the curve reaches L/2 | |
| Euler's number, the base of the natural logarithm |
About this formula
- FieldMathematics
- TopicFunctions and growth models
- LevelUniversity
- Also calledlogistic growth model, logistic curve, sigmoid function, S-curve, logistic growth formula
- SourceWikidata Q1052379
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