Free tool
Work out the final cell count, the number of generations or the generation time for a culture in exponential (log) phase, using Nn = N0 x 2^n. The working is shown with your numbers substituted.
Built for MicrobiologyCells or CFU. Use the same unit for the final count.
Use the same unit for the generation time and the elapsed time.
Enter the known values.
Growth-curve phases and the counting formulas are easy to blur together. Encodr keeps them on a spaced-repetition schedule so the math is there when the exam asks for it.
Get started freeBacteria divide by binary fission, so each generation doubles the population: Nn = N0 x 2^n, where
N0 is the starting count, Nn is the final count and n is the number of generations. The generation time (also
called the doubling time) is the time for one complete round of fission, so g = t / n. To get n from
two counts, rearrange with logs: n = log10(Nn / N0) / log10(2).
These formulas describe exponential (log) phase only. A real culture also has a lag phase before it, and a stationary phase and death phase after it, where the doubling math no longer holds.
Worked example: a single cell (N0 = 1) that divides every 30 minutes for 24 hours has 1,440 / 30 = 48 generations, so Nn = 1 x 2^48 = about 2.8 x 10^14 cells. Going the other way, a culture that grows from 1.0 x 10^6 to 8.0 x 10^6 cells in 120 minutes has n = log10(8) / log10(2) = 3 generations, so g = 120 / 3 = 40 minutes. The full walkthrough is in the bacterial growth curve and generation time, and the whole course is in the free Microbiology deck.
How bacteria grow: the four phases of the growth curve, binary fission, and the generation-time formulas Nn = N0 x 2^n and g = t / n, with worked examples.
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