63. Samples of bacterial culture taken at 5 PM and then the next day at 5 AM were found
to have 104 and 107 cells·mL−1, respectively.
Assuming that both the samples were taken during the log phase of cell growth,
the generation time of this bacterium will be __________ h.
Introduction
Understanding the generation time of bacteria during log phase is a fundamental concept in microbiology
and is frequently tested in competitive examinations such as GATE, CSIR-NET, and other life science entrance exams.
This article provides a detailed solution to a Numerical Answer Type (NAT) question with clear mathematical steps
and conceptual explanations.
Question Overview
Samples of a bacterial culture were taken at:
- 5 PM: 104 cells/mL
- Next day at 5 AM: 107 cells/mL
Assuming both samples were taken during the log (exponential) phase of growth,
calculate the generation time of the bacterium.
Step-by-Step Solution
Step 1: Calculate the Time Interval
From 5 PM to 5 AM the next day:
Time interval = 12 hours
Step 2: Calculate the Number of Generations
During log phase, bacterial growth follows the equation:
N = N0 × 2n
Where:
- N0 = 104
- N = 107
N / N0 = 107 / 104 = 103 = 1000
2n = 1000
n = log2(1000) ≈ 9.97 ≈ 10 generations
Step 3: Calculate the Generation Time
Generation time (g) is given by:
g = Total time / Number of generations
g = 12 / 9.97 ≈ 1.2 hours
Final Answer
Generation time = 1.2 hours
Key Takeaways for Exams
- Log phase growth follows binary fission (2n rule).
- Always calculate the number of generations before calculating generation time.
- NAT questions require precise numerical calculations.
Conclusion
The generation time of bacteria during log phase in this problem is
1.2 hours. Understanding exponential growth equations ensures accuracy
in numerical microbiology problems.
