Henderson's Dictionary of Biological Terms, by Eleanor Lawrence. 10th Ed.
Evolutionary Ecology, by Eric R. Pianka, 3rd Ed.
Population sizes changes due to a number of different factors. Storms, fires and hurricanes can reduce a population drastically. An influx of highly nutritious food can lead to a population upsurge.
If a population with a constant growth rate increases linearly with respect to time. In this case, you can calculate its growth rate with the following formula:
Graph 1 shows the results of a linear growth rate, where 10 individuals are added to the population each year.
where Nt is the number of individuals at time t, and N0 is the number of individuals at time = 0. This is a simple type of population growth. Populations may also grow exponentially, following this formula:
Graph 2 shows an exponential growth rate, where r = 2.25.
Populations will see an exponential growth when there is bountiful resources, such as living space and food. But at a certain size, those resources will limit how fast a population can grow, until the population reaches some upper limit for its habitat. The sigmoidal curve of the Pearl-Verhulst logistic equation:
shows such a situation, where N is the number of individuals at a given time in the population, K is the carrying capacity of the habitat, and r is the unlimited growth rate of the population.
Graph 3 shows how a population size alters as it reaches the limits of its habitat. This type of growth is very typical of bacteria growth in a laboratory. We may expect this type of growth in any population who does not face factors that could reduce their numbers below the carrying capacity of the habitat.