Logistic Growth Calculator
Model logistic (S-curve) growth with a carrying capacity. Used for population modeling.
Population
599.86
सूत्र
## 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.
हल किया गया उदाहरण
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
अक्सर पूछे जाने वाले प्रश्न
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.
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