In binary fission, a parent cell divides to form two daughter cells. Thus, bacterial population increase exponentially. Note the table below, demonstrating how quickly a population of bacteria can explode from just a single cell. The generation (first, second, third, etc) is denoted n and the number of cells at a given time is N (or N0 at time zero).
| Generation (n) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | n |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Formula | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 210 | 211 | 2n-1 |
| # of Cells (N) | 1 | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 1024 | 2048 | N |
The table below describes important formulas regarding population dynamics. They are valid for any value of x, as long as it is kept constant throughout the problem. Also, t is elapsed time and td is the time require for one complete cell division (for a cell to double).
| Important Formulas | ||||||
| N = N02n | ||||||
| logx N = logx N0 + n (logx 2) | ||||||
| logx (N / N0) = n (logx 2) | ||||||
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| N = N0 antilog10 (.301n) | ||||||
| n = t / td |
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