The S-shaped growth curve is also called a logistic growth curve. It describes a situation in which (in a new environmental condition) the population density of an organism increases slowly establishing itself then increasing rapidly, approaching an exponential growth rate. Many population of micro-organisms broadly follow this basic sigmoidal pattern. For example, when a fresh culture medium is inoculated with bacteria, sigmoidal or S-shaped growth curve is observed. The S-shaped curve is generated when a population approaches the environmental's carrying capacity. Carrying capacity is the maximum number of individuals of a population that can be supported in a given time.The S-shaped growth form is represented by the following equation- Ã¢â‚¬Â dN/dt = rN[K-N/K]Where, r = intrinsic rate of natural increase, N = population density at time t and K = carrying capacity.