Question

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

Answer 1

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.

Answer 2

Answer:

4% is the growing rate of Cape Coral-Fort Myers from 2000 to 2010.

a simplified version