Population Growth Calculator
Exponential Growth
Unlimited growth model: Nt = N0 × e^(rt)
Logistic Growth
Growth with carrying capacity: Nt = K / (1 + ((K-N0)/N0) × e^(-rt))
Formula
Exponential: Nt = N₀ × e^(rt). Logistic: Nt = K / (1 + ((K−N₀)/N₀) × e^(−rt)). Doubling time = ln(2)/r. Max dN/dt at N = K/2.
Frequently Asked Questions
What is the difference between exponential and logistic growth?
Exponential growth assumes unlimited resources: Nt = N₀e^(rt), producing J-shaped curves. Logistic growth includes a carrying capacity K that limits population size, producing S-shaped (sigmoid) curves.
What is intrinsic growth rate (r)?
The intrinsic rate of natural increase (r) is the per-capita growth rate under ideal conditions: r = birth rate − death rate. A positive r means the population is growing.
When does logistic growth rate peak?
The population growth rate (dN/dt) in logistic growth is maximum when the population is at K/2 (half the carrying capacity). At this point, dN/dt = rK/4.
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