The population of a bacteria culture doubles every 2 minutes. Approximately…
2026
The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?
Answer: D. 18 — Concept: When a quantity doubles every fixed interval, it follows exponential growth given by the geometric-progression relation N = N0 × 2n, where N0 is the…
- A.
10
- B.
12
- C.
14
- D.
18
Attempted by 29 students.
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Correct answer: D
Concept: When a quantity doubles every fixed interval, it follows exponential growth given by the geometric-progression relation N = N0 × 2n, where N0 is the initial value and n is the number of doubling periods elapsed; here each doubling period lasts 2 minutes. Solve for n first, then convert n into minutes.
Application:
Set up the growth equation: N0 × 2n = N, i.e. 1,000 × 2n = 500,000.
Divide both sides by 1,000: 2n = 500.
Compare with powers of 2: 29 = 512, the power of 2 closest to 500, so n ≈ 9 doubling periods.
Convert doubling periods to time: each period is 2 minutes, so total time = 9 × 2 = 18 minutes.
Cross-check: Substituting n = 9 back gives 1,000 × 512 = 512,000, close to the target of 500,000 (the question asks for an approximate time), confirming 18 minutes as the best-supported option among those offered.
