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) = (154305)/(102286)`

`lne ^(10x) = ln( (154305)/(102286) )`

`10x=ln( (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.