Bacterial Doubling
Exponential bacterial growth by generations.
Formula
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Doubles each generation
How it works
This formula estimates how many bacteria are present after a period of growth when the population divides into two at regular intervals. It works because each generation multiplies the population by 2, so after t/g generations the total increase is 2 raised to that number of doublings, starting from the initial count N_0. In real cultures, this models the exponential phase where conditions are ideal and resources are not yet limiting.
When to use it
Use this when a bacterial population is growing by binary fission with a known generation time, such as in a lab culture or a simplified microbiology problem. It is most appropriate during exponential growth, not when nutrients, space, or waste buildup slow the population down.
Worked example, step by step
Suppose a culture starts with N_0 = 500 bacteria and the generation time is g = 20 minutes. After t = 2 hours, the elapsed time is 120 minutes. Number of generations = t / g = 120 / 20 = 6 Apply the formula: N = N_0 × 2^(t/g) N = 500 × 2^6 N = 500 × 64 N = 32,000 bacteria
Common mistakes to avoid
- Using the wrong time units for t and g, such as mixing hours with minutes
- Forgetting that the exponent is the number of generations, so t must be divided by g first
- Applying the formula to all growth situations, even when the bacteria are in the lag or stationary phase
Did You Know?
At 3% annual growth a population doubles in about 23 years, a pace that reshapes cities within a lifetime.
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