To solve this problem, we need to understand the concept of a logistic growth curve and its asymptote.$\newline$The logistic growth model is represented by the equation:$\newline N(t) = \frac{K}{1 + \left(\frac{K - N_0}{N_0}\right)e^{-rt}} \newline$where:$\newline \bullet N(t)$ is the population size at time $t \newline \bullet K$ is the carrying capacity of the environment$\newline \bullet N_0$ is the initial population size$\newline \bullet r$ is the intrinsic growth rate$\newline$In a logistic growth curve, the population grows rapidly at first, then slows as it approaches the carrying capacity, K.$\newline$The asymptote of the logistic growth curve is the value that the population size approaches as time goes to infinity.$\newline$This asymptote is the carrying capacity, K.$\newline$Therefore, the asymptote is obtained when the population size, N, equals the carrying capacity, K.$\newline$Thus, the correct option is:$\newline$Option 1: K = N