A population of bacteria starts with 100 cells and grows by binary fission. If the doubling time is 30 minutes, how many cells will there be after 3 hours?
Answer
6400
The correct answer is 6400 — Compute 2^6 = 64; multiply: 100 × 64 = 6400.
Step-by-step solution
- Find number of doubling periods: 3 hours = 180 minutes; doubling every 30 min → 180/30 = 6 periods.
- Use formula N = N0 × 2^n: N0 = 100, n = 6 → N = 100 × 2^6.
- Compute 2^6 = 64; multiply: 100 × 64 = 6400.
Common mistake: Using 3 hours as 3 doubling periods instead of 6
Concept tested: Exponential growth via binary fission
Published · How this solution was prepared and checked
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