Q.What is sigmoid curve ?

The sigmoid curve is the S-shaped logistic growth curve a population follows as it approaches the carrying capacity (K) of its environment.

In nature, no population has unlimited resources indefinitely; food, space and other resources become limiting as population size grows. The pattern of growth under such limited-resource conditions, when plotted as population size (N) against time, produces a characteristic S-shaped (sigmoid) curve, described by the Verhulst-Pearl logistic growth equation:

dN/dt = rN (1 - N/K)

where N = population size, r = intrinsic rate of natural increase, t = time, and K = carrying capacity (the maximum population size the environment can sustain).

Phases of the sigmoid curve:

1. Lag phase -- growth is slow initially as the population establishes itself.
2. Exponential (log) phase -- growth accelerates rapidly as resources are still abundant and the (1 - N/K) term is close to 1. …