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 now 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 5000 and less than 10000 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.
a. Let's choose the town of Pleasantville. Using the second column, the expression for the current estimated population of Pleasantville in terms of x is x. Using the third column, the expression for the current estimated population in terms of x is x - 0.02x = 0.98x.
b. Adding Concord to the table:
Concord p -9%
To find the expressions for the current estimated population of Concord in terms of p, we need to use the percentage change -9%.
Using the second column, the expression for the current estimated population of Concord in terms of p is p. Using the third column, the expression for the current estimated population in terms of p is p - 0.09p = 0.91p.
c. Let's choose p = 6000.
To calculate the estimated current population of Concord, we need to use the expression 0.91p = 0.91 * 6000 = 5460. Based on the chosen percentage change of -9%, the estimated current population of Concord is 5460. This expression was used because it accounts for the decrease in population by multiplying the initial population by the percentage change (0.91).