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

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

In this equation, dN/dt is the rate at which the population grows. The factor (K − N)/K slows the growth as the population comes close to the carrying capacity.

Option (1) Population density at time t — Incorrect. The population density at time t is written as N, not r.

Option (2) Population density at time Zero — Incorrect. The starting density is written as N₀. It appears in the integral form of exponential growth, N_t = N₀e^rt, not in this equation.

Option (3) Intrinsic rate of natural increase — Correct. r is the birth rate minus the death rate per individual (r = b − d). It is the population’s own power to grow, and it is used to judge how any factor affects growth.

Option (4) Carrying capacity — Incorrect. The carrying capacity is K, the largest population the habitat can support.

Note: The same question was also asked in CUET (UG) 2026 on 29-05-2026 (Slot 2), and a similar question in CUET (UG) 2026 on 19-05-2026 (Slot 1).

NCERT Extract:
Population Growth – “… In nature, a given habitat has enough resources to support a maximum possible number, beyond which no further growth is possible. Let us call this limit as nature’s carrying capacity (K) for that species in that habitat. 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 Since resources for growth for most animal populations are finite and become limiting sooner or later, the logistic growth model is considered a more realistic one.”

Figure 11.3 Population growth curve a when responses are not limiting the growth, plot is exponential, b when responses are limiting the growth, plot is logistic, K is carrying capacity