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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 bestfit line from excel which was 0.014 (figure 1).
I took the average of 0.0159 and 0.014 with the assumption that 0.0159 was too high a
k
value.
The
average
k
was 0.015.
My final differential equations were:
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This note was uploaded on 04/29/2008 for the course MATH 310 taught by Professor Mcnamara during the Spring '08 term at Saint Louis.
 Spring '08
 MCNAMARA
 Math

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