Carrying capacity in the given equation of logistic growth is represented by :
\( \displaystyle dN/dt = rN\left(\frac{K-N}{K}\right) \)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → K
In the logistic equation, K is the carrying capacity. This is the largest number of individuals of a species that a habitat can support with its resources. The fraction \( \displaystyle \frac{K-N}{K} \) shows how much room is left. When N reaches K, this fraction is zero and growth stops.
(1) dN/dt — Incorrect. This is the rate of change of the population size with time.
(2) rN — Incorrect. This is the growth rate when resources are unlimited (exponential growth).
(3) r — Incorrect. This is the intrinsic rate of natural increase, which is birth rate minus death rate per individual.
(4) K — Correct. This is the carrying capacity.
NCERT Extract:
Population Growth –
