Q.58 If a bacterial culture with a doubling time of 30 minutes starts with two cells, then
the number of cells after 4 hours are _______.
Bacterial cultures exhibit exponential growth during binary fission, where the population doubles every generation. With a doubling time of 30 minutes starting from two cells, the culture reaches 512 cells after 4 hours. This calculation uses the formula N=N0×2n, where n is the number of generations.
Step-by-Step Calculation
Convert 4 hours to minutes: 4×60=240 minutes. Divide by doubling time: n=240/30=8 generations.
Starting with N0=2 cells, apply the exponential growth equation: N=2×28.
Since 28=256, final count is 2×256=512 cells. Track growth: after 1st (30 min): 4 cells; 2nd: 8; up to 8th: 512.
Growth Pattern Table
| Time (hours) | Generations | Cells |
|---|---|---|
| 0 | 0 | 2 |
| 1 | 4 | 32 |
| 2 | 8 | 512 |
| 3 | 12 | 8192 |
| 4 | 16 | 131072 |
Common MCQ Options Explained
No explicit options appear in the query, but CSIR NET-style questions often include distractors like 256, 1024, or 64. Option like 256 mistakes initial 1 cell instead of 2, yielding 1×28=256.
Choices like 1024 assume 9 generations (2×29=1024), ignoring exact 240/30=8. Linear growth errors (e.g., 16 cells) fail to account for compounding.
CSIR NET Exam Relevance
This tests microbial growth kinetics in Unit 1 (Cellular Organization) of CSIR NET Life Sciences. Understand phases: lag, log (exponential), stationary, death—focus here is log phase.
Practice variations: if doubling time 20 min, n=12, cells=8192. Use for quantitative genetics, biotech culture optimization.
