Calculatrice de Croissance Logistique Gratuite
Modélisez la croissance logistique d'une population. Calculez l'évolution avec une capacité d'accueil maximale.
Population
599.86
Formule
Logistic Growth Model
Formula
P(t) = K / (1 + ((K - P₀) / P₀) × e^(-rt))
Where:
S-Curve
Logistic growth starts exponentially, slows as it approaches the carrying capacity, and levels off. The inflection point (fastest growth) occurs at P = K/2.
Exemple Résolu
Population starting at 10, carrying capacity 1000, growth rate 0.5, at time t = 10.
- 01P(10) = 1000 / (1 + 99 × e^(-5))
- 02= 1000 / (1 + 99 × 0.00674)
- 03= 1000 / (1 + 0.667)
- 04= 1000 / 1.667 ≈ 599.71
Questions Fréquentes
What is logistic growth?
Logistic growth is a model where a population grows exponentially at first, then slows as it approaches a maximum (carrying capacity). It produces an S-shaped curve.
What is the carrying capacity?
The carrying capacity (K) is the maximum population size that the environment can sustain indefinitely, limited by resources, space, and competition.
Where is logistic growth used?
Population biology, epidemiology (disease spread), market saturation models, technology adoption curves, and bacterial growth in limited environments.
Apprendre