According to the Verhulst-Pearl logistic growth model, the rate of change in population size is given by the equation dN dt = rN ( K-N K ) . When the population density ( N ) exactly reaches the carrying capacity ( K ) of the habitat, what will be the value of the environmental resistance term ( K-N K ) and the corresponding population growth rate ( dN dt ) respectively?

Step-by-step solution

In the Verhulst-Pearl logistic growth equation, dN dt = rN ( K-N K ) , the term ( K-N K ) represents the environmental resistance. When the population density ( N ) reaches the carrying capacity ( K ), we substitute N = K into the term: K-K K = 0 K = 0 Consequently, the population growth rate becomes: dN dt = rN 0 = 0 This mathematical boundary condition indicates that the population size has stabilized and is no longer growing, which corresponds to the asymptote of the logistic growth curve. Answer: 0 and Zero