How to Use Exponents in the Ecosystem
In any typical ecosystem, a population size for a given organism grows exponentially provided there are enough resources. As long as factors such as food, shelter and predators do not limit growth, a population's size increases rapidly over time, since more living organisms means more organisms are available to reproduce. Exponential growth over time is governed by the birth rate, death rate, the initial population size and the exponential function "e," sometimes written "exp." The human population is currently undergoing a state of exponential growth, and its future population can be estimated using the exponential growth method.
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Instructions
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Calculate the birth rate by dividing the total number of births in the most recent year by the population size at the end of that year. In the United States this number was 0.0143 in 2007.
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Determine the death rate by taking the ratio of deaths to total population size. This number was 0.00763 for the United States in 2007.
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Subtract the death rate from the birth rate to obtain the rate of natural increase. Continuing the example, you have 0.00667.
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Multiply by the rate of natural increase by number of years from now you want to know the population to get the argument of the exponential function. If you want to know the population in 50 years, you multiply 0.00667 by 50, yielding 0.3335.
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Take the exponential of the argument and then multiply by the initial population to arrive at the larger future population. The exponential key on a scientific calculator is usually denoted "e to the power x." The x is the argument of the exponential. The number "e" is approximately 2.71828, so if you don't have an exponential key on your calculator, raise 2.71828 to the power 0.3335. The population of the United States in 2007 was 302 million. You then take the exponential of 0.3335, which is 1.396, and multiply it by 302.2 million for a projected population of 421.9 million in 2057.
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Tips & Warnings
The number "e" appears nearly as frequently in mathematics as the number pi..
References
- Photo Credit crowd at the stadium image by Christopher Meder from Fotolia.com
