What is the difference between exponential and logistic growth?

Exponential growth and logistic growth represent two fundamental patterns of population change. Exponential growth occurs when a population increases at a constant percentage rate without environmental constraints, following the formula dN/dt = rN. This creates a J-shaped curve where growth accelerates continuously. In nature, exponential growth typically occurs when populations are small, resources are abundant, or species colonize new habitats.

Logistic growth, conversely, incorporates environmental limitations through carrying capacity (K)—the maximum population size an environment can sustain. The logistic equation is dN/dt = rN((K-N)/K), which produces an S-shaped curve. Growth is exponential when the population is small, slows as resources become limited, and eventually plateaus near carrying capacity. Most natural populations, from bacteria to butterflies, exhibit logistic growth because environments have finite resources. Understanding this distinction helps ecologists predict population trajectories, manage wildlife populations, and assess ecosystem health.