In Verhulst-Pearl logistic growth equation – dN/dt = rN ≤ft((K - N)/K…

The correct answer is Option (3) → Intrinsic rate of natural increase

In a growing population the change in number per unit time is dN/dt = rN, where r = b − d. Here b is the birth rate and d is the death rate per individual. The logistic equation adds the factor (K − N)/K, which slows the growth as the population gets near the limit of the habitat.

(1) Population density at time ‘t’ — Incorrect. This is N, the number of individuals present at time t.

(2) Carrying capacity — Incorrect. The carrying capacity is the maximum population that the habitat can support. It is shown by K.

(3) Intrinsic rate of natural increase — Correct. r is the intrinsic rate of natural increase. It is the birth rate minus the death rate per individual. A larger r means that the population can grow faster.

(4) Population density at time zero — Incorrect. The equation has no symbol for the starting density. It gives only the rate of change.

Note: The same question was also asked in CUET (UG) 2022 on 20-08-2022 (Slot 1), and a similar question in CUET (UG) 2026 on 19-05-2026 (Slot 1), and in CUET (UG) 2025 on 14-05-2025 (Slot 2).

NCERT Extract:
Population Growth – “… A population growing in a habitat with limited resources show initially a lag phase, followed by phases of acceleration and deceleration and finally an asymptote, when the population density reaches the carrying capacity. A plot of N in relation to time (t) results in a sigmoid curve. This type of population growth is called Verhulst-Pearl Logistic Growth (Figure 11.3) and is described by the following equation:”
\( \displaystyle\frac{dN}{dt} = rN\left(\frac{K-N}{K}\right) \)
“Where N = Population density at time t
r = Intrinsic rate of natural increase
K = Carrying capacity”