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Math lab 1.4

Math lab 1.4 - Victor Liou Dr McNamara Math Lab 1.4(North...

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Victor Liou Dr. McNamara 02/16/2007 Math Lab 1.4 (North Carolina) This project involved analysis of population data of North Carolina between the years of 1790 and 2000. For the first question, I determined as accurately as possible an exponential growth model to predict the population of North Carolina in the year 2010. The differential equation and solution of exponential growth are as follows: = , ( )= . dydt ky y t Aekt With the population data, I was able to substitute in values to solve for the parameters A and k which represent the initial population and growth rate coefficient, respectively. By setting = t 0 for the initial time point, I found that = A 394 . Since solving for k between subsequent decades yielded different values, I decided to average three k values to use for my equation. By substituting = , t 10 110 and 210 , I solved the equation = y 394ekt and got k values of . , . , . . 0 01932 0 01427 and 0 01437 averaging these values, I found k to be 0.0159. This value is similar to value given by the exponential best-fit line from excel which was 0.014 (figure 1).

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