Question 3
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.
To find the current estimated population of Pleasantville, we can use the equation: x + (x * (-2/100)).
To find the current estimated population of Amity Center, we can use the equation: y + (y * (5/100)).
To find the current estimated population of Harmony Corners, we can use the equation: z + (z * (7/100)).
Adding a fourth row to the table for Concord, we have:
Concord p -9%
To find the current estimated population of Concord, we can use the equation: p + (p * (-9/100)).
Let's choose p = 7,500.
Using the expression: 7,500 + (7,500 * (-9/100)), we can calculate the estimated current population of Concord.
7,500 + (7,500 * (-9/100)) = 7,500 - 675 = 6,825.
Therefore, the estimated current population of Concord is 6,825.
We use the expression p + (p * (-9/100)) because the given percentage change for Concord is -9%, expressing a decrease in population. By calculating p + (p * (-9/100)), we calculate the decrease in population from the previous census. The negative sign in front of the percentage change accounts for the decrease in population.