NEET2026BiologyChapterActual
According to the Verhulst-Pearl logistic growth model, a plot of population density ( N ) against time ( t ) yields a sigmoid curve. At which of the following stages does this growth curve reach its asymptote?
Options
- AWhen the population density ( N ) reaches exactly half of the carrying capacity ( K )
- BWhen the population density ( N ) becomes equal to the carrying capacity ( K )
- CWhen the intrinsic rate of natural increase ( r ) drops to zero
- DWhen the environmental resistance becomes negligible
Correct answer
B. When the population density ( N ) becomes equal to the carrying capacity ( K )
Step-by-step solution
The Verhulst-Pearl logistic growth is described by the equation dN dt = rN ( K - N K ) . Here, N is the population density at time t , r is the intrinsic rate of natural increase, and K is the carrying capacity. A plot of N against t results in a sigmoid curve. The asymptote of this curve represents the maximum population size that the environment can sustain. This occurs when the population density ( N ) becomes equal to the carrying capacity ( K ), making dN dt = 0 . Thus, the growth curve reaches its asymptote w