Each generation doubles the count
Bacteria split in two, so the population multiplies rather than adds. t / Td is simply how many doublings fit in the elapsed time. Ten doublings is a factor of 1,024; twenty is over a million. That is why a warm food left out spoils so fast.
Doublings and the resulting count
| Doublings (t / Td) | Multiplier | From 1 cell |
|---|---|---|
| 1 | 2× | 2 |
| 5 | 32× | 32 |
| 10 | 1,024× | ~1 thousand |
| 20 | 1,048,576× | ~1 million |
| 30 | ~1.07 billion× | ~1 billion |
To count doublings backwards from a known population: doublings = log₂(N / N₀). To reach a target N, that many doublings times Td is the time.
Typical doubling times at 37°C
| Organism | Doubling time |
|---|---|
| E. coli (rich medium) | ~20 min |
| Salmonella | 25–30 min |
| Staphylococcus aureus | 25–30 min |
| Listeria monocytogenes | 30–40 min |
| Clostridium botulinum | 30–60 min |
These are lab-optimal figures. A poorer medium or a cooler temperature stretches the doubling time to an hour or more, which is the whole point of refrigeration.
Common questions
How long for one E. coli cell to reach a million?
A million is about 20 doublings (2 to the 20th is roughly 1.05 million). At a 20-minute doubling time that is about 400 minutes, or just under 7 hours, under ideal lab conditions.
What is the difference between doubling time and growth rate?
Doubling time is a concrete span, like 20 minutes. Growth rate r is the constant in the exponential form. They are linked: r equals the natural log of 2 divided by the doubling time, so a 20-minute doubling gives r of about 0.035 per minute.
Does bacteria growth stay exponential forever?
No. Doubling only holds during the log phase, when food is plentiful and waste is low. Before it comes a slow lag phase, and after it the culture hits a stationary phase and then decline as nutrients run out and waste builds up.
