When a small inoculum of bacteria is placed in a fresh batch culture — a test tube, a flask, or the petri dish shown here — the population does not grow at a constant rate forever. Plotting cell count against time produces a characteristic S-shaped curve with four named phases: lag, exponential (log), stationary, and death. All four phases fall out of a single logistic growth equation once nutrient depletion and cell death are added.
r, following dN/dt = r·N·(1 − N/K), where K is the carrying capacity set by nutrient supply.K as nutrients run low and waste products accumulate; division roughly balances death.K: richer medium supports a larger colony and a longer stationary phase.This four-phase curve, first formalized in the early 20th century, still underlies how microbiologists time antibiotic dosing, how food scientists set shelf-life limits, and how bioreactor operators decide exactly when to harvest a culture at its productive peak.
A single logistic equation drives a 3D petri-dish colony through the four classic phases of bacterial growth — lag, exponential, stationary and death — as you adjust nutrient supply and temperature.
The colony's population follows dN/dt = r·N·(1 − N/K) during growth, then declines exponentially once nutrients run out — the same shape microbiologists plot on real growth curves.
Set nutrient supply and temperature, then watch the colony spread across the dish while the live graph traces population against elapsed time, colour-coded by phase.
Food scientists use this exact curve to set expiry dates: refrigeration doesn't kill bacteria, it just pushes the lag phase out for days or weeks.