Population Dynamics

Exponential Growth

How many time periods?

Starting population
(100 to 500)

Growth rate
(between 0 and 4)

About This Graph

When a population has unlimited resources its numbers can increase at an ever increasing rate. This type of growth is called exponential growth. The above graph lets you explore this simple form of growth by adjusting the initial population size and the growth rate. Enter new values in the text boxes and click the “Apply changes” button. You can also choose how far into the future you want to calculate by selecting one of the four time period buttons.

The horizontal axis on the graph is the time axis and the vertical axis is the population size. Note that the scale on the vertical axis changes to match the calculated values. Pay close attention to the vertical scale when comparing graphs. You can mouse over points on the graph to read values for each point.

Time periods are arbitrary. The time axis just shows population change over time. No particular time units are used. You could assign different meanings to the time periods to suit your purpose. For bacteria that reproduce every twenty minutes, for example, each time period could be thought of as a twenty minute interval. For White-tailed Deer that typically give birth once a year, you might choose to think of a time period as a year.

Starting population is the number of individuals in the population at the beginning. The allowed range of from 100 to 500 individuals has been arbitrarily chosen to allow for some variety in explorations and to minimize artifacts resulting from mathematical simplifications.

Growth rate is the rate of population increase when there are no limiting factors. A value of 1 means no increase, i.e. just enough individuals are born or immigrate into the environment to replace those that die or emigrate. A rate of 1.5 means the population is increasing by 50% each time interval, and so on.