Exponential: N = N₀e^(rt) | Logistic: N = K/(1+((K-N₀)/N₀)e^(-rt))
Two fundamental models: Exponential growth (N = N₀e^(rt)) assumes unlimited resources — populations grow without bounds. This applies to early colonization, invasive species, and bacteria in fresh media. Logistic growth (N = K/(1+((K-N₀)/N₀)e^(-rt))) adds carrying capacity K — growth slows as N approaches K, producing an S-shaped curve. Real populations often oscillate around K due to time lags. The intrinsic growth rate r = birth rate − death rate. Human population: r ≈ 1.1%/year, doubling time ≈ 63 years. World population grew from 1 billion (1800) to 8 billion (2022). Understanding these models is essential for wildlife management, conservation, epidemiology, and resource planning.