Bot 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. Chart: Town: Pleasantville, Amity Center, Harmony Corners, blank. Census Population: x, y, z, blank. Percentage Change: -2%, +5%, +7%, blank.
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.
a. Let's choose the town of Pleasantville.
Using the second column, the current estimated population of Pleasantville can be expressed as x + ((-2/100) * x).
Using the third column, the current estimated population of Pleasantville can be expressed as (1 + (-2/100)) * x.
b. We will add a fourth row to the table for the town of Concord.
For Concord's population, let's assume it was p people at the last census.
Let's choose a percentage change of -9% for Concord.
Using the second column, the current estimated population of Concord can be expressed as p + ((-9/100) * p).
Using the third column, the current estimated population of Concord can be expressed as (1 + (-9/100)) * p.
c. Let's choose a value of p as 6,500 for the population of Concord.
Using the expression (1 + (-9/100)) * p, we can calculate the estimated current population of Concord.
(1 + (-9/100)) * 6,500 = 0.91 * 6,500 = 5,915.
Rounding this to the nearest whole number, we estimate the current population of Concord to be 5,915.
We used this expression because the given percentage change was -9%, which means a decrease in population. By multiplying p with (1 + (-9/100)), we account for the decrease in population based on the chosen percentage change.