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) |
|
|
|
|
| N = N0 antilog10 (.301n) |
|
| n = t / td |
