Exponential Growth Model

Assuming that in any time interval (dt) an individual can be added to the population either through birth or immigration and in the same interval there is a probability of dying or emigrating, then the instantaneous rate of per capita growth will be r = b — d

where r represents the intrinsic rate of growth for the population at time t. The differential equation representing the increase in population size during successive time intervals is dN df rN

where N represents the population size and r represents the population's intrinsic capacity for increase (also referred to as the Malthusian parameter). This model assumes that environmental resources are unlimited and r is a constant. The population will increase as long as r is positive (i.e., as long as b> d) (A, Figure 3).

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