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Exponential Decay of African Elephants

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Jen Middleton

on 4 January 2013

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Transcript of Exponential Decay of African Elephants

By Natalie Maus and Jen Middleton Elephant Population Table Equation Correlation Coefficient The population of African Elephants has been decreasing at an alarming rate for the past century. For example, in the 1800's there were about 10 million African Elephants, but by 1993, that number dropped to about half a million! The goal of this project was to create an equation to represent the exponential decrease in these elephants population. Then we can predict how long we have until these amazing animals will go extinct. Using the data from the table, we were able to create an exponential equation to model the data:
y=ab^x
y=the population of African Elephants
x= the number of years after 1900 a=12106888.11
b=0.9701839449

Final Equation: y=12106888.11(0.9701839449)^x The correlation coefficient for this equation is 0.9429554475. This means that this equation fits the data very well, because correlation coefficient measures how close the points are to the line created by the equation. A perfect correlation would have a correlation coefficient of 1, so the closer the value is to one, the better the data correlates to the equation. In this case, 0.9429554475 is very close to one, so the equation fits the data very well. Next, the percent of the data points that are actually on the line created by the equation is 0.8891649759, or 88.91649759%. This means that the majority of the data fits exactly on the line created by the equation. In conclusion, this equation we are using to model the decrease in the elephant population fits well with the data we found. Graph: African Elephants Exponential Decay Predictions Usually, in an exponential decay graph, there is an asymptote, or a number that the line will get closer and closer too, by never actually touch. In the graph modeled by our equation, the asymptote would be y=0. Realistically though, there is no asymptote for this data, because if the elephant population continues to decline at this rate, they will become extinct. Based on our equation, if we don't do anything to help the African Elephants, there will be just over 1,000 of them left by the year 2200, and they will become completely extinct by the year 2439. For course that seems like a long way into the future, but there's no reason why we shouldn't start helping now! Thanks For Watching!! Bibliography
"African Elephants." African Elephants. N.p., n.d. Web. 12 Dec. 2012
"Elephant." Elephant. N.p., n.d. Web. 12 Dec. 2012.
Mogadishu, Somalia., Jeffrey Gettleman; Isma'il Kushkush Contributed Reporting From Omdurman, Sudan; Mia Li From Beijing; And A Somali Journalist From. "Elephants Dying in Epic Frenzy As Ivory Fuels Wars and Profits." The New York Times. The New York Times, 04 Sept. 2012. Web. 12 Dec. 2012.
N.p., n.d. Web.
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