Q.82 At t = 0, the bacterial cell number is 10,000 cells/mL. At t = 480 minutes, the cell
number increased to 320,000 cells/mL. The mean generation time during this
exponential growth period, rounded off to the nearest integer is ________ minutes.
The mean generation time for the bacterial population is 96 minutes. This calculation uses the standard formula for exponential growth during the log phase.
Calculation Steps
Bacterial growth follows N = N₀ × 2n, where N is the final cell number (320,000 cells/mL), N₀ is the initial number (10,000 cells/mL), and n is the number of generations.
Solve for n: n = log₂(N/N₀) = log₂(320000/10000) = log₂(32) = 5 generations.
Mean generation time g = t/n = 480/5 = 96 minutes, rounded to the nearest integer.
Verification
The population increased 32-fold in 480 minutes, exactly 5 doublings (since 25 = 32). Each doubling thus takes 480/5 = 96 minutes, confirming exponential growth without lag or stationary phases affecting the result.
Introduction to Bacterial Growth Generation Time
Bacterial growth generation time calculation is essential for CSIR NET Life Sciences exams, measuring doubling time during exponential phase. In this case, bacterial cell number rises from 10,000 cells/mL at t=0 to 320,000 cells/mL at t=480 minutes, yielding a mean generation time of 96 minutes.
Exponential Growth Formula Explained
Use N = N₀ × 2g, rearranged as g = t/log₂(N/N₀), where g is generation time in minutes. Here, log₂(32) = 5, so g = 480/5 = 96.
- Matches E. coli-like rapid growth (20-30 min typical, but varies by conditions).
- Assumes pure log phase, no nutrient limits.
Step-by-Step Solution for CSIR NET
- Compute fold increase: 320,000/10,000 = 32x.
- Generations
n = log₂(32) = 5. g = 480/5 = 96minutes (nearest integer).
Common errors: Forgetting log base-2 or including non-exponential phases.
Calculation Parameters Table
| Parameter | Value | Formula Role |
|---|---|---|
| Initial (N₀) | 10,000 cells/mL | Starting population |
| Final (N) | 320,000 cells/mL | End population |
| Time (t) | 480 min | Duration |
| Generations (n) | 5 | log₂(32) |
| Generation time | 96 min | t/n |
Exam Tips & Variations
For CSIR NET, verify exponential phase data. Variations: Slower growers like Mycobacterium (hours) vs. fast like Vibrio (15 min). Practice with OD600 graphs for real labs.
