Which one of the followings is the correct equation for describing Ve…

The correct answer is Option (2) → \( \displaystyle\frac{dN}{dt} - rN\left(\frac{K-N}{K}\right) \)

In nature, resources are limited, so a population cannot grow without limit. Verhulst-Pearl logistic growth describes this. The rate of growth of the population is written as:

    \( \displaystyle\frac{dN}{dt} = rN\left(\frac{K-N}{K}\right) \)

Here N is the population density at time t, r is the intrinsic rate of natural increase and K is the carrying capacity, the largest population the habitat can support. When N is small, (K − N)/K is close to 1 and growth is almost exponential. As N moves towards K, the factor falls to zero and the growth stops.

(1) \( \displaystyle\frac{dt}{dN} = N\left(\frac{K-N}{N}\right) \) — Incorrect. It gives time per unit change of N, not the rate of change of N. It has no r and no K in the denominator.

(2) \( \displaystyle\frac{dN}{dt} - rN\left(\frac{K-N}{K}\right) \) — Correct. It has the logistic form: the growth rate dN/dt, the term rN and the factor (K − N)/K.

(3) \( \displaystyle\frac{dt}{dN} = d\left(\frac{K-N}{N}\right) \) — Incorrect. It also has dt/dN. The symbol d is not the growth rate r.

(4) \( \displaystyle\frac{dN}{dt} - N\left(\frac{N-K}{K}\right) \) — Incorrect. The factor (N − K)/K is negative when N is below K. It would show a falling population instead of a rising one. It also has no r.

Note: A similar question was also asked in CUET (UG) 2026 on 29-05-2026 (Slot 1), in CUET (UG) 2025 on 30-05-2025 (Slot 1), and in CUET (UG) 2024 on 29-05-2024 (Slot 1).