A population growing in a habitat with limited resources shows a Verhulst-Pearl logistic growth. Under which of the following mathematical conditions does the population growth curve reach its asymptote?

Step-by-step solution

A population growing in a habitat with limited resources shows initially a lag phase, followed by phases of acceleration and deceleration and finally an asymptote, when the population density reaches the carrying capacity. The Verhulst-Pearl logistic growth is described by the equation dN dt = rN ( K - N K ) . The asymptote is reached when the population growth rate ( dN dt ) becomes zero. This occurs when the population density ( N ) equals the carrying capacity ( K ). Mathematically, when N = K , the ratio N K =