A population growing in a habitat with limited resources shows logistic growth curve

Asymptote in a logistic growth curve is obtained when K = N. Let's understand why.

Logistic Growth Curve

The logistic growth curve is a type of S-shaped curve used in population ecology to model the growth of populations. It takes into account the carrying capacity of the environment and assumes that population growth rate decreases as the population approaches the carrying capacity.

Asymptote

An asymptote is a line that a curve approaches but never touches. In the context of the logistic growth curve, the asymptote represents the carrying capacity of the environment, which is the maximum population size that the environment can sustain.

K and N

K (carrying capacity) and N (population size) are two important parameters in the logistic growth model. K represents the maximum population size that the environment can sustain, while N represents the current population size.

Asymptote and K = N

When the current population size (N) is equal to the carrying capacity (K), the logistic growth curve reaches its maximum value, which is the carrying capacity. At this point, the growth rate of the population becomes zero, and the population size stabilizes.

Therefore, when K = N, the logistic growth curve approaches the carrying capacity asymptotically and reaches a stable equilibrium. This is why option A is the correct answer.