Question

a. 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. b. 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. c. Explain the similarities and differences between your equations in (a) and (b). d. During what year will the population of city (a) first exceed that of city (b)? Show all of your work and explain your steps. e. 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.

Answer 1

Answer: You have a lot of work to do here. I can get you started in the right direction.

The growth equation that you are looking for will be in the form of:
 y = a(1 + b)^x.
A is the starting amount, b is the percent that you are increasing by and x is the number of years.

The declining equation that you are looking for will be in the form of:
y = a(1 - b)^x.
Again, a is the starting amount, be is the percent that you are decreasing by and x is the number of years.

I suggest you find an online graphing calculator and graph each equation. Then, you can answer the rest of your questions.