For this example I am going to use Cape Coral-Fort Myers Florida which was the fastest growing city of 2017.
As of January of 2000, the population of the city was 102,286, and as of January 1 of 2010, the population was 154,305; therefore, I'm going to examine a population growth over a period of 10 years.
I am going to use the standard model for population growth:
y=N _{0} e ^{rx}
Where:
x= time (in years)
r= growth rate
N _{0} = initial population
y= population after a time x
Now, I'm going to replace the values in the equation to get r:
154305=102286e ^{10x}
e^{10x} = \frac{154305}{102286}
lne ^{10x} = ln( \frac{154305}{102286} )
10x=ln( \frac{154305}{102286} )
x= 0.04
Finally, I will multiply x by 100% to obtain 4% which the growing rate of Cape Coral-Fort Myers from 2000 to 2010.
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