Q.79 Ten bacteria were inoculated into a rich medium. If at the end of
ten hours the total number of cells is 104, then the number
of elapsed generations and the generation time respectively is
Options:
- (A) 10, 120 minutes
- (B) 10, 60 minutes
- (C) 20, 30 minutes
- (D) 40, 15 minutes
Bacterial Growth Calculation: Elapsed Generations and Generation Time
Numerical problems based on bacterial growth kinetics are frequently asked in
NEET, CUET, AIIMS, and Class 11–12 Biology exams. These questions test concepts of
binary fission, exponential growth, elapsed generations, and generation time.
Concept Used
Bacteria reproduce by binary fission, resulting in exponential growth.
The standard growth equation is:
N = N0 × 2n
- N = final number of cells
- N0 = initial number of cells
- n = number of generations
Step-by-Step Solution
Given:
- Initial number of cells, N0 = 10
- Final number of cells, N = 104
- Total time = 10 hours
Step 1: Calculate Number of Generations
Using the growth equation:
104 = 10 × 2n
103 = 2n
n = log(103) / log(2)
n = 3 / 0.301 ≈ 9.97 ≈ 10 generations
Step 2: Calculate Generation Time
Generation time (g) is calculated as:
g = Total Time / Number of Generations
g = 10 hours / 10 = 1 hour = 60 minutes
Final Answer
Elapsed generations = 10
Generation time = 60 minutes
Correct Option: (B)
Quick Revision Formula
| Quantity | Formula |
|---|---|
| Number of generations | n = log(N / N0) / log(2) |
| Generation time | g = t / n |
Conclusion
This numerical problem demonstrates the application of exponential growth principles in
bacterial populations. With correct use of formulas and logical steps, such questions
become easy scoring in competitive exams.
