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Population size does not reach an equilibrium phase at any time shaped growth curve has three phases-establishment phase, exponential phase and crash phase.

Establishment or initial phase is also called lag phase. There is a slow rise in population as the initial size of the population is small. As the population size reaches a take off stage, it enters the second phase called exponential or log phase. During this phase the population size rises rapidly. The increase is so rapid that soon the population size grows much beyond the carrying capacity of the environment. A point is reached when population declines suddenly due to mass scale deaths. It is called crash phase. J shaped growth form of population occurs in those cases where either the food chains are short or there is excessive human interference, It occurs in many insect population. They show explosive increase in number during the rainy season but almost disappear towards the end of the season.

Exponential growth form can be represented mathematically by the following exponential equation

dN/dt=(B-D)x N

dN/dt is the rate of change in population size, B is the birth rate,D is the death rate and N is the population size.

Let (B-D) =r is the intrinsic rate of natural increase

Then dN/dt=rN.

Exponential Growth Curve