Population Growth
Model how a population grows: unlimited exponential growth, or logistic growth that levels off at the carrying capacity. Solve for the population size, starting size, growth rate, time or capacity.
How do Populations Grow?
When food and space are unlimited, every individual reproduces at the same rate, so growth is proportional to the population: exponential growth. Bacteria in fresh broth and invasive species in a new habitat grow this way — at first.
Real environments have limits. In the logistic model growth slows as the population approaches the carrying capacity K, producing the characteristic S-shaped curve. Growth is fastest at N = K/2.
Live Graph
exponentialDoubling Times
| Organism / population | Doubling time | r |
|---|---|---|
| E. coli (ideal conditions) | 20 min | 2.08 /h |
| Baker’s yeast | 90 min | 0.46 /h |
| Human cells in culture | ~24 h | 0.029 /h |
| Rabbits (no predators) | ~6 months | 1.4 /yr |
| World population (2020s) | ~80 years | 0.009 /yr |
Key Relations
The growth rate per individual, r, is constant. The population multiplies by the same factor in every equal time step.
The factor (1 − N/K) slows growth as resources run out. Near zero it behaves exponentially, near K growth stops.
A population growing at 1% per year doubles in about 70 years; at 7% in about 10 years.
Sources & Verification
- N. J. Gotelli, A Primer of Ecology, 4th ed., Sinauer, 2008 — chapters “Exponential Population Growth” and “Logistic Population Growth”.