In a habitat with limited resources, a population exhibits Verhulst-Pearl logistic growth. The growth curve reaches an asymptote when:

Step-by-step solution

The Verhulst-Pearl logistic growth is described by the equation dN dt = rN (1 - N K ) , where N is the population density, r is the intrinsic rate of natural increase, and K is the carrying capacity. The growth curve reaches an asymptote when the population size stops increasing, meaning the growth rate dN dt becomes zero. Setting dN dt = 0 gives 1 - N K = 0 , which implies N = K . Thus, the asymptote is reached when the population density ( N ) equals the carrying capacity ( K ). Answer: the population density ( N