In the Verhulst-Pearl logistic growth equation, \( r \) is defined as:
\( \displaystyle \frac{dN}{dt} = rN\left(\frac{K-N}{K}\right) \)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Intrinsic rate of natural increase
In the logistic growth model, a population grows fast at first, then slows down, and finally levels off at the carrying capacity (K), the largest number the habitat can support. In the equation, N is the population density at time t, K is the carrying capacity, and r is the intrinsic rate of natural increase. It is the rate at which the population would grow if nothing limited it. The factor (K − N)/K slows the growth as N gets closer to K.
(1) Intrinsic rate of natural decrease — Incorrect. There is no such term. r measures how fast the population increases.
(2) Intrinsic rate of natural increase — Correct. This is what r stands for.
(3) Population density — Incorrect. Population density is N in the equation, not r.
(4) Extrinsic rate of natural increase — Incorrect. There is no such term. r is intrinsic, because it is a property of the population itself.
Note: A similar question was also asked in CUET (UG) 2026 on 29-05-2026 (Slot 2), and in CUET (UG) 2022 on 20-08-2022 (Slot 1).
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
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