How fast bacteria multiply
One cell that divides every 30 minutes would, with unlimited food, become 281,474,976,710,656 cells in 24 hours.
Generation time
For people, a generation is the time from one point in life to the same point in the next generation, about 25 years. That idea does not work well for bacteria, which can divide quickly or stay dormant for thousands of years. For bacteria and archaea the generation time is defined as the time it takes the population to double through one round of binary fission, so it is also called the doubling time.
Doubling times vary enormously. OpenStax gives E. coli as little as 20 minutes under the best laboratory conditions, though the same species may need several days in a harsh environment. Mycobacterium tuberculosis takes 15 to 20 hours, and M. leprae about 14 days. Temperature, nutrients and pH all change the rate, but for a given species in given conditions the generation time is fixed by its genes.
Counting the cells
If cells divide at a steady rate, the number after n generations is the starting number times 2 to the power n: N = N₀ × 2ⁿ. Here n is the elapsed time divided by the generation time. OpenStax works through an example. A single cell that divides every 30 minutes goes through 48 divisions in 24 hours, so it gives 2⁴⁸ = 281,474,976,710,656 cells, which is easier to write as 2.8 × 10¹⁴. A second example starts with 1 × 10⁵ cells, a doubling time of 30 minutes and 2 hours of growth: that is 4 generations, so 10⁵ × 2⁴ = 1.6 × 10⁶ cells.
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On an ordinary scale this kind of growth looks flat for most of the graph and then shoots up at the end, because each step adds as many cells as already exist. Microbiologists usually plot the logarithm of the cell number instead. On a log scale, each doubling moves the line up by the same amount, so steady exponential growth becomes a straight line and its slope shows the growth rate.
The growth curve in a flask
No real culture keeps doubling for long. When a few cells are put into fresh broth in a closed flask, the number of live cells follows a curve with four phases. In the lag phase the number hardly changes: the cells are growing larger, making the proteins they need for the new medium and repairing any damage. In the log, or exponential, phase they divide steadily at their generation time. As nutrients run low, waste builds up and oxygen is used up, growth slows and stops: in the stationary phase new cells are made as fast as old ones die. Finally, in the death phase, cells die faster than they divide and the number falls.
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- Generation (doubling) time: time for the population to double.
- N = N₀ × 2ⁿ, with n = time ÷ generation time.
- Log scale turns steady doubling into a straight line.
- Closed culture: lag, log, stationary, death.
- One cell divides every 30 minutes. How many generations in 24 hours?
- So how many cells after 24 hours, with unlimited food?
- About 2.8 × 10¹⁴
- About 48
- About 2,304
- About 1 million
- Start with 100,000 cells, doubling time 30 minutes, 2 hours of growth. How many cells? (write the full number)
- E. coli doubling every 20 minutes, starting from one cell: how many cells after 8 hours?
- In a continuous exponential growth model with a 20-minute doubling time, about how many hours does one cell take to pass 1 million? (one decimal place)
- In which phase are cells adjusting to fresh medium without increasing in number?
- Lag phase
- Log phase
- Stationary phase
- Death phase
- Why does growth stop in the stationary phase?
- Nutrients run low and waste builds up, so births equal deaths
- All the cells have died
- The cells become viruses
- The light is turned off
- Order the phases of a closed bacterial culture.
- On a semilogarithmic graph, steady exponential growth looks like…
- a straight rising line
- a flat line
- a curve that bends down
- a circle
- Which has the longest doubling time, according to OpenStax?
- Mycobacterium leprae (about 14 days)
- E. coli in the lab (20 minutes)
- Mycobacterium tuberculosis (15 to 20 hours)
- They are all equal
Sources for this course (15)
- OpenStax Microbiology 1.1 What Our Ancestors Knew (fermented drink from rice, honey and fruit in Neolithic China by 7000 BC, Saccharomyces cerevisiae in bread, Leeuwenhoek 1675 "animalcules" in rain water, Golden Age of Microbiology 1857 to 1914; openstax.org/books/microbiology/pages/1-1-what-our-ancestors-knew)
- 1.3 Types of Microorganisms (about 100 µm to see with the eye, animal cell about 10 µm, bacteria about 1 µm, viruses about 100 nm, three domains, coccus/bacillus/spirillum, archaea without peptidoglycan and in extreme places such as Morning Glory pool, protists, algae, diatoms 2 to 200 µm, protozoa with cilia, flagella or pseudopods, fungi with chitin walls, more than 1000 yeast species, molds and penicillin, helminths, prions about one-tenth of a virus; .../1-3-types-of-microorganisms)
- 3.1 Spontaneous Generation (Aristotle, van Helmont's mice recipe of 3 weeks, Redi 1668 with six jars, Needham 1745, Spallanzani, Pasteur 1858 gun-cotton filter, swan-neck flasks, Alhumbert Prize 1862, 1864 lecture; .../3-1-spontaneous-generation)
- 3.2 Foundations of Modern Cell Theory (Semmelweis 1847, 10 to 20 percent vs 1 percent, chlorinated lime; Snow; Pasteur 1856 fermentation; Lister 1867 carbolic acid; Koch's postulates; .../3-2-foundations-of-modern-cell-theory)
- 6.1 Viruses (acellular, obligate intracellular parasites, DNA or RNA never both, capsid, envelope, spikes, helical/polyhedral/complex, 20 nm to 900 nm, Ivanovski 1892 with the Chamberland filter of 1884, pore 0.1 µm, Beijerinck 1898 and virus = poison, Stanley 1935, host range, bacteriophages, FDA 2006 phage spray on lunch meats; .../6-1-viruses)
- 9.1 How Microbes Grow (binary fission, FtsZ Z ring, generation time, E. coli 20 minutes, human generation 25 years, M. tuberculosis 15 to 20 hours, M. leprae 14 days, 2^48 = 281,474,976,710,656 after 24 h at 30 minutes, Nn = N0 2^n, lag/log/stationary/death, budding, fragmentation, Epulopiscium; .../9-1-how-microbes-grow)
- Royal Society: Philosophical Transactions 12:821-831, published 25 March 1677, Leeuwenhoek's Dutch letter of 9 October 1676 "concerning little animals" (doi.org/10.1098/rstl.1677.0003)
- Royal Society archive EL/L1/22 (letter to Oldenburg dated at Delft, 18 pages, partial translation by Oldenburg)
- Royal Society blog "Celebrating Leeuwenhoek", 2023 (first letter via de Graaf, Phil. Trans. 19 May 1673; 190 letters in fifty years; died 26 August 1723 aged 90)
- N. Lane 2015, Phil. Trans. R. Soc. B 370:20140344 (upwards of 1,000,000 creatures in a drop of pepper-water; letter read aloud over several sessions)
- Lens on Leeuwenhoek, letter L-040 (Oldenburg printed less than half; Hooke succeeded later in 1677)
- CDC MMWR 53(34):783, 2004, 150th Anniversary of John Snow and the Pump Handle (31 August 1854, handle removed 8 September 1854, Vibrio cholerae isolated 1883; cdc.gov/mmwr/preview/mmwrhtml/mm5334a1.htm)
- CDC History of Smallpox and Smallpox timeline (Jenner 1796; 33rd World Health Assembly declared the world free of smallpox on 8 May 1980; cdc.gov/smallpox/about/history.html)
- American Chemical Society, Discovery and Development of Penicillin landmark (Fleming 1928 at St Mary's Hospital London, paper June 1929, Florey and Chain at Oxford from 1939; acs.org/education/whatischemistry/landmarks/flemingpenicillin.html)
- Fleming 1929, Br J Exp Pathol 10:226. Sender, Fuchs and Milo 2016, PLoS Biol 14:e1002533 (3.8 × 10^13 bacteria and 3.0 × 10^13 human cells in a 70 kg reference man, ratio about 1.3, bacteria about 0.2 kg).
Checked: 2026-10-17