Calculate bacterial population growth, generation time, and growth rates using exponential growth models. Plot growth curves and analyze bacterial growth phases.
Primary Result
--
Number of Generations
--
Doubling Time
--
Specific Growth Rate (μ)
--
Generation time (also called doubling time) is the time required for a bacterial population to double in size during exponential growth phase. It varies by species - E. coli has ~20 minutes, while M. tuberculosis takes 12-24 hours.
During the log phase, bacteria divide by binary fission at constant intervals. Each cell splits into two identical cells, causing the population to double with each generation: 1→2→4→8→16→32, following the equation N(t) = N₀ × e^(rt).
Bacterial growth occurs in four phases: lag phase (adaptation), log phase (exponential growth), stationary phase (growth plateaus), and death phase (population declines). Most calculations focus on the exponential log phase.
Growth rate (r) can be calculated using r = ln(N/N₀)/t, where N is final population, N₀ is initial population, and t is time elapsed. Alternatively, r = ln(2)/generation_time for exponential growth.
Temperature, pH, nutrient availability, oxygen levels, and bacterial species all influence growth rate. Optimal conditions maximize growth rate, while stress conditions slow or halt growth.
Calculations assume ideal exponential growth conditions. Real bacterial cultures may deviate due to nutrient depletion, waste accumulation, or environmental changes. Results are most accurate during the log phase.
Growth rate (r) is the natural logarithm rate of increase, while specific growth rate (μ) represents the fractional increase per unit time. They're related by μ = r, but μ is often expressed as doublings per hour.