Bacterial Growth Calculator

Bacterial growth/decay: N(t) = N₀·e^(rt)

Bacterial populations grow along exponential kinetics N(t) = N₀·e^(rt), where r is the intrinsic growth rate. Doubling time t_d ties back to r through r = ln(2)/td. Give E. coli ideal conditions and it doubles every 20 min (r ≈ 0.0347/min). Start with a single cell and 8 hours later you would expect 2²⁴ ≈ 16 million cells. Of course nutrients and space run short, which is why the logistic model dN/dt = rN(1 − N/K), with carrying capacity K, fits the whole curve. Going the other way, decay from antibiotics or sterilization obeys first-order kinetics N(t) = N₀·e^(−kt). Here the decimal reduction time D = ln(10)/k tells you how long it takes to knock the population down by 90 %. Pasteurization at 72 °C for 15 s cuts pathogens by 4–5 log, while an autoclave at 121 °C for 15 min guarantees a reduction of ≥12 log (sterility assurance level 10⁻⁶).

Applications

You will run into it in clinical microbiology (sepsis kinetics, MIC determination), in pharmaceutical sterilization (autoclave validation, D and Z values), and in food preservation (pasteurization, UHT, cold chain). It also drives industrial fermentation (yeast, lactic acid, antibiotic production), wastewater treatment, and biotechnology, where recombinant proteins get expressed in fed-batch reactors.

FAQ

Why doesn't bacterial growth stay exponential forever? Nutrients run out, waste piles up, and quorum sensing switches the cells into stationary-phase metabolism. So the curve moves through its lag, log, stationary, and death phases instead of climbing without end.

What's the difference between bacteriostatic and bactericidal? A bacteriostatic agent just stops growth (r ≈ 0). A bactericidal one actively kills the cells, giving k > 0 and a net decay.

How do I compute generations elapsed? Use n = t/t_d, which makes N(t) = N₀·2ⁿ. So with t_d = 20 min and t = 2 h you get n = 6 generations and N = 64·N₀.