In a population with no immigration or emigration, the rate of change in population size over time over a defined time interval is a function of the difference between the rates of birth and death. When the birthrate exceeds the death rate, the rate of population change increases with population size. As the time interval over which population change is evaluated decreases, approaching zero, the change in population size is expressed as a continuous function, and the resulting pattern is termed exponential population growth. The difference in the instantaneous per capita rates of birth and death is defined as r, which is the instantaneous per capita growth rate.