## Math in the Natural Sciences## Math and the Environment |

## How is mathematics used to describe population growth of organisms in a certain environment? |

In general, a certain population of organisms—from rabbits to humans—will grow exponentially if it is left unchecked. That means that in a “perfect world” a population’s rate of increase is constant. This can be seen in the following equations:

- after 1 year = P
_{0}(1 +*r*) - after 2 years = P
_{0}(1 +*r*)^{2} - after 3 years = P
_{0}(1 +*r*)^{3}…

- after
*n*years = P_{0}(1 +*r*)^{n}

in which P_{0} is the population today and *r* is the rate of increase. These equations are further modified for population growth statistics, but such intricate calculations are not within the scope of this book. (For more about population growth and biology, see above.)