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Logistic growth

Generalized logistic growth fits y = K / (1 + exp(−r · (x − x₀))), where K is the carrying capacity, r the growth rate and x₀ the inflection point.

What is Logistic growth?

The classic Verhulst logistic — symmetric S-curve. Originated as a population-growth model (population approaches a carrying capacity K limited by resources).

When should I use Logistic growth?

  • Population dynamics.
  • Adoption / diffusion curves.
  • Any symmetric saturating growth.

What data does it need?

Numeric time X + Y.

What does it report?

K + r + x₀ with CIs.

How do I interpret the result?

Without observations beyond the inflection, K (carrying capacity) is poorly identified — report wide CIs honestly.

See also

References

  • Verhulst (1838). Notice sur la loi que la population suit dans son accroissement. Corresp. Math. Phys. 10.