In the Logistic Growth Model,as the Number of Individuals in the Population

In the logistic growth model,as the number of individuals in the population (N) approaches the carrying capacity (K) ,the rate of growth (dN/dt)

A) increases rapidly until N far surpasses K.
B) increases rapidly until N reaches K and then stops.
C) increases at the same rate it has been,continuing on until N is beyond K for some distance before regulating.
D) approaches zero as N approaches K.
E) stops well before N reaches K and stabilizes.