Bacterial Growth Formula
Calculate bacterial population size after multiple generations of binary fission.
Used in microbiology and lab work.
The Formula
N = N₀ × 2ⁿ
Bacteria reproduce by binary fission — each cell splits into two. This formula calculates the total number of bacteria after n generations of division.
Variables
| Symbol | Meaning |
|---|---|
| N | Final number of bacteria |
| N₀ | Initial number of bacteria |
| n | Number of generations (divisions) |
To find generations from time: n = t / g, where t = total time and g = generation time (time per division).
Example 1
Starting with 100 bacteria, how many after 8 generations?
N = 100 × 2⁸
N = 100 × 256
N = 25,600 bacteria
Example 2
E. coli divides every 20 minutes. Starting with 1 cell, how many after 4 hours?
n = 240 minutes / 20 minutes = 12 generations
N = 1 × 2¹² = 4,096
N = 4,096 bacteria after 4 hours
When to Use It
Use the bacterial growth formula when:
- Predicting bacterial colony size in lab experiments
- Estimating contamination growth over time
- Understanding how quickly infections can spread
- Planning antibiotic treatment timing