Question

**PLEASE HURRY**

1. 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.
2. Find another city whose population starts larger than the city in part (a), but
that during this same time experienced population decline. Determine its
population for January 1st of the same year you picked for part (a). Write an
exponential function to represent the city’s population, y, based on the
number of years that pass, x after a period of population decline. Describe
the variables and numbers that you used in your equation.
3. Explain the similarities and differences between your equations in (a) and
(b).
4. During what year will the population of city (a) first exceed that of city (b)?
Show all of your work and explain your steps.
5. During what year will the population of city (a) be at least twice the size of
the population of city (b)? Show all of your work and explain your steps.
PLEASE USE PARIS AND CHICAGO FOR THE CITIES

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:

Where:

= time (in years)

= growth rate

= initial population

= population after a time

Now, I'm going to replace the values in the equation to get :

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