When resources such as food and space are unlimited, a population can realise its innate growth potential and increase exponentially. Its increase is proportional to its current size: dN/dt = rN. Plotting N against time gives a J-shaped curve in the textbook idealisation. The integrated model is N(t) = N(0)e^(rt), with e the natural exponential base and r the intrinsic rate of natural increase.

The curve assumes suitable constant conditions and no effective resource limitation; it is not a universal trajectory for nature. If a simplified discrete organism doubles each interval, successive sizes are N, 2N, 4N and 8N, illustrating geometric increase, not the exact continuous model. Always check whether the question asks for continuous exponential growth, a doubling illustration or logistic growth with carrying capacity K.

Worked example: Four starting Paramecium becoming eight after one doubling and sixteen after another illustrates rapid ideal increase.

NCERT trap: J-shaped growth describes an unlimited-resource model; finite habitats impose constraints.

NEET method: Identify resource conditions and curve shape before inserting numbers into the appropriate formula.

Reading estimate; allow another 3–5 minutes for each set of three checks.

Organisms and Populations

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