A county planner prepares the following table showing population trends in three local towns. The first column gives the name of the town. The second column gives the population as of the last census. The third column gives the estimated increase or decrease in population since that census, expressed as a percentage of the previous population. Town Population Percentage Change Pleasantville x –2% Amity Center y +5% Harmony Corners z +7% Choose one of these towns. Use the information from the second and third columns to write two expressions showing the current estimated population of the town in terms of x, y, or z. Add a fourth row to the table showing the population information for the town of Concord. Concord’s population as of the last census was p people; for its percentage change, choose a negative integer not divisible by two. Write two expressions showing the current estimated population of Concord in terms of p. Choose a number greater than 5,000 and less than 10,000 for the value of p. Based on the percentage change you chose in part b) above, calculate the estimated current population of Concord, rounding to the nearest whole number if needed. Explain why you used the expression you did to make your calculation.

Question

A county planner prepares the following table showing population trends in three local towns. The first column gives the name of the town. The second column gives the population as of the last census. The third column gives the estimated increase or decrease in population since that census, expressed as a percentage of the previous population. Town Population Percentage Change Pleasantville x –2% Amity Center y +5% Harmony Corners z +7% Choose one of these towns. Use the information from the second and third columns to write two expressions showing the current estimated population of the town in terms of x, y, or z. Add a fourth row to the table showing the population information for the town of Concord. Concord’s population as of the last census was p people; for its percentage change, choose a negative integer not divisible by two. Write two expressions showing the current estimated population of Concord in terms of p. Choose a number greater than 5,000 and less than 10,000 for the value of p. Based on the percentage change you chose in part b) above, calculate the estimated current population of Concord, rounding to the nearest whole number if needed. Explain why you used the expression you did to make your calculation.

Answer 1

One expression showing the current estimated population of Pleasantville in terms of x would be:

Population of Pleasantville = x + (0.98)x
This expression takes the previous population (x) and decreases it by 2% (0.98x).

Another expression showing the current estimated population of Amity Center in terms of y would be:
Population of Amity Center = y + (1.05)y
This expression takes the previous population (y) and increases it by 5% (0.05y).

Adding a fourth row to the table for Concord:
Town Population Percentage Change
Concord p -3%

Two expressions showing the current estimated population of Concord in terms of p would be:
Population of Concord = p + (-0.03)p
or
Population of Concord = p - (0.03)p
Both of these expressions take the previous population (p) and decrease it by 3% (-0.03p).

Let's assume p = 6000. Using the expression Population of Concord = p + (-0.03)p, we can calculate the estimated current population of Concord as follows:
Population of Concord = 6000 + (-0.03)(6000)
= 6000 - 180
= 5820
Since the percentage change is negative (-3%), we subtract the decrease from the previous population to calculate the estimated current population.