Asymptote is a logistic growth curve is obtained when

When K = N in a logistics growth curve, it is an asymptote.
It means a population growing in a habitat with limited resources show initially an Iag phase, followed by a phase of acceleration and deceleration and finally an asymptote, i.e. when the population density (N)reaches the carrying capacity (K)

Population growth curve rs logistic,
when responses are limiting the growth, here K is carrying capacity and N is population density.