Q74. A growing bacterial culture with a doubling time of 20 min reaches cell density of 2 × 108 cells/ml in 3 hours. How much time would it take to reach the cell density of 1 × 106 cells/ml?
Questions based on bacterial growth kinetics are very common in microbiology exams.
These problems use the concept of doubling time and exponential cell division.
Let us solve this numerical step-by-step in the simplest way.
Concept Used – Exponential Growth Formula
Bacteria divide by binary fission and follow exponential growth:
N = N0 × 2n
- N = final population
- N0 = initial population
- n = number of generations
- n = t / g
- g = doubling time
Step-by-Step Solution
Step 1 – Calculate number of generations in 3 hours
3 hours = 180 minutes
Doubling time (g) = 20 minutes
n = 180 / 20 = 9 generations
Step 2 – Calculate initial population
2 × 108 = N0 × 29
29 = 512
N0 = (2 × 108) / 512 ≈ 3.9 × 105
Step 3 – Find generations needed to reach 1 × 106
Ratio = (2 × 108) / (1 × 106) = 200
2n = 200 ≈ 28
n ≈ 8 generations
Step 4 – Convert generations into time
t = n × g
t = 8 × 20 = 160 minutes
Correct Answer: C. 160 minutes
Quick Exam Trick
Use directly:
t = g × log2 (N / N0)
This saves time during competitive exams.
Key Takeaways
- Bacterial growth is exponential
- Use N = N0 × 2n
- Generations = time / doubling time
- Always compare ratios for faster calculation
