Asymptote in a logistic growth curve is obtained when

The logistic growth curve is a type of S-shaped curve that represents the growth of a population that approaches a maximum value, known as the carrying capacity (K) of the environment. The carrying capacity is the maximum population size that the environment can support sustainably.

When the population size (N) equals the carrying capacity (K), the population growth rate approaches zero, and the curve approaches a horizontal line that is referred to as the asymptote. This is because the resources available in the environment become limited and cannot support any further population growth.
(2) When K>N, the population would still be growing until it reaches the carrying capacity, at which point it would level
Off and reach the asymptote.
(3) K<N is incorrect because the population showing logistic growth cannot grow beyond the carrying capacity, at which
Point, it would level off and reach the asymptote.
(4) The intrinsic rate of natural increase (r) of a species is constant and does not change over time.