a. Let's choose the town of Pleasantville.
The current estimated population of Pleasantville can be expressed as x - (2% of x) or as (1 - 0.02)x.
b. Adding a row for Concord:
Town Census Population Percentage Change
Pleasantville x -2%
Amity Center y +5%
Harmony Corners z +7%
Concord p -9%
The current estimated population of Concord can be expressed as p - (9% of p) or as (1 - 0.09)p.
c. Let's choose p = 7,500 as the value for Concord's last census population.
Using the expression (1 - 0.09)p, the estimated current population of Concord would be:
(1 - 0.09) * 7,500 = 0.91 * 7,500 = 6,825.
I used the expression (1 - 0.09)p to calculate the estimated current population of Concord because the percentage change given for Concord was -9%. To calculate the estimated current population, I multiplied the last census population (p) by the remaining percentage after the decrease (-9%), which is equivalent to multiplying p by (1 - 0.09).
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 Census Population Percentage Change
Pleasantville x –2%
Amity Center y +5%
Harmony Corners z +7%
a. Choose one of these towns. Use the second and third columns to write two
expressions showing the current estimated population of the town in terms of
x, y, or z.
b. 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.
c. 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, 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
1 answer