Organisms And Populations
A bacterial population with an intrinsic rate of natural increase of 0.69 per hour grows exponentially; approximately how long will the population take to double in size?
Select the correct option:
Solution
1 hour
Exponential growth in an unlimited resource environment is described by dN/dt = rN, whose integrated form is Nt = N0 e^(rt). The doubling time is obtained when Nt/N0 = 2, giving rt = ln 2 = 0.693, so t = 0.693 / r. Substituting r = 0.69 per hour, t = 0.693 / 0.69 ≈ 1.0 hour. Hence the population doubles in roughly one hour. The option 2 hours is wrong because it would correspond to r ≈ 0.347 per hour, half the given value. The option 0.5 hour is incorrect since it implies r ≈ 1.39 per hour. The option 4 hours would require r ≈ 0.173 per hour, which contradicts the data. As explained in NCERT Class 12, Chapter 13 (Organisms and Populations), r is the intrinsic rate of natural increase and is a key parameter for assessing the impact of environmental factors on population growth. Plausibility check: a value of r close to ln 2 conveniently yields a doubling time near unity, and since doubling time is inversely proportional to r, the answer is dimensionally and biologically consistent.
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About This Question
- Subject
- biology
- Chapter
- ecology and environment
- Topic
- organisms and populations
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
1 hour
Exponential growth in an unlimited resource environment is described by dN/dt = rN, whose integrated form is Nt = N0 e^(rt). The doubling time is obtained when Nt/N0 = 2, giving rt = ln 2 = 0.693, so t = 0.693 / r. Substituting r = 0.69 per hour, t = 0.693 / 0.69 ≈ 1.0 hour. Hence the population doubles in roughly one hour. The option 2 hours is wrong because it would correspond to r ≈ 0.347 per hour, half the given value. The option 0.5 hour is incorrect since it implies r ≈ 1.39 per hour. The option 4 hours would require r ≈ 0.173 per hour, which contradicts the data. As explained in NCERT Class 12, Chapter 13 (Organisms and Populations), r is the intrinsic rate of natural increase and is a key parameter for assessing the impact of environmental factors on population growth. Plausibility check: a value of r close to ln 2 conveniently yields a doubling time near unity, and since doubling time is inversely proportional to r, the answer is dimensionally and biologically consistent.
This medium difficulty biology question is from the chapter ecology and environment, covering the topic of organisms and populations. It appeared in the 2025 exam.
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