Q.53
A culture of 106 bacteria, with doubling time of 60 min, is grown in a nutrient medium at 37 °C. Considering that the nutrients are unlimited, the number of bacteria at the end of 10 h would be _____ × 106.
The number of bacteria after 10 hours is 1024 × 10^6. This result comes from exponential growth under unlimited nutrients, where the population doubles every 60 minutes.
Calculation Steps
Bacterial growth follows the formula Nt=N0×2t/Td, where N0=106 is the initial count, t=10 hours = 600 minutes is the total time, and Td=60 minutes is the doubling time.
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Number of doublings: 600/60=10.
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Final count: 106×210=106×1024=1.024×109, or 1024 × 10^6.
At 37°C with unlimited nutrients, the culture stays in the exponential phase, supporting this precise doubling.
Introduction to Bacterial Growth
Bacterial growth in nutrient medium at 37°C follows exponential kinetics when nutrients are unlimited, making bacteria doubling time 60 min 10 hours a key calculation for competitive exams like CSIR NET Life Sciences. Starting from a culture of 10^6 bacteria, precise doubling predicts massive population expansion, vital for molecular biology and microbiology studies.
Exponential Growth Formula Explained
Use Nt=N0×2n, where n=t/Td. Here, t=600 min and Td=60 min give n=10, so Nt=106×1024=1024×106.
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Doublings occur every 60 min under ideal 37°C conditions.
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No lag, stationary, or death phases apply due to unlimited nutrients.
Step-by-Step Solution
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Convert time: 10 h = 600 min.
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Compute doublings: 600 / 60 = 10.
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Apply growth: 210=1024.
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Multiply: 106×1024=1024×106.
This matches E. coli-like growth at 37°C in rich media.
Exam Relevance for CSIR NET
Such problems test bacteria doubling time 60 min 10 hours in unlimited nutrient scenarios, emphasizing binary fission and generation time. No options are provided, but common distractors include miscounting doublings (e.g., 10 h / 1 h = 10, correct; errors like 9 or 11 yield 512 × 10^6 or 2048 × 10^6).
| Common Error | Doublings Assumed | Result (× 10^6) | Why Wrong |
|---|---|---|---|
| 9 doublings | 540 min only | 512 | Ignores full 600 min |
| 10 doublings | Exact 600 min | 1024 | Correct |
| 11 doublings | Extra hour | 2048 | Overcounts time |
| Linear growth | +10^6/h | 11 | Ignores exponential |
Practical Applications
In labs, 37°C optimizes growth for biotech like recombinant DNA work. Track via OD600; doubling time confirms log phase. For CSIR NET, master this for genetics and microbiology sections.
