Organisms And Populations

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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?

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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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