Logistic Growth Calculator — Formel
## Logistic Growth Model
### Formula
**P(t) = K / (1 + ((K - P₀) / P₀) × e^(-rt))**
Where:
- **K** = carrying capacity (maximum population)
- **P₀** = initial population
- **r** = intrinsic growth rate
- **t** = time
### 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.
### Formula
**P(t) = K / (1 + ((K - P₀) / P₀) × e^(-rt))**
Where:
- **K** = carrying capacity (maximum population)
- **P₀** = initial population
- **r** = intrinsic growth rate
- **t** = time
### 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.
Lösungsbeispiel
Population starting at 10, carrying capacity 1000, growth rate 0.5, at time t = 10.
- P(10) = 1000 / (1 + 99 × e^(-5))
- = 1000 / (1 + 99 × 0.00674)
- = 1000 / (1 + 0.667)
- = 1000 / 1.667 ≈ 599.71