Do some research and find a city that has experienced population growth. Determine its population on January 1st of a certain year. Write an exponential function to represent the city’s population, y, based on the number of years that pass, x after a period of exponential growth. Describe the variables and numbers that you used in your equation

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:
[tex]y=N _{0} e ^{rx} [/tex]
Where:
[tex]x[/tex]= time (in years)
[tex]r[/tex]= growth rate
[tex]N _{0} [/tex]= initial population 
[tex]y[/tex]= population after a time [tex]x[/tex]

Now, I'm going to replace the values in the equation to get [tex]r[/tex]:
[tex]154305=102286e ^{10x} [/tex]
[tex]e^{10x} = \frac{154305}{102286} [/tex]
[tex]lne ^{10x} = ln( \frac{154305}{102286} )[/tex]
[tex]10x=ln( \frac{154305}{102286} )[/tex]
[tex]x= 0.04[/tex]

Finally, I will multiply x by 100% to obtain 4% which the growing rate of Cape Coral-Fort Myers from 2000 to 2010.