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
Pleasantville Amity Center Harmony Corners
Census Population
x y z
Percentage Change
–2% +5% +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.
Let's choose the town "Pleasantville" and use the second and third columns to write expressions for its current estimated population.
The second column states that the population of Pleasantville as of the last census is x.
The third column states that the estimated population increase or decrease since that census is -2% of the previous population. To calculate this, we multiply -2% by x.
Therefore, the expression for the current estimated population of Pleasantville would be x + (-2% * x) or x - (0.02 * x).
So, the expression for the current estimated population of Pleasantville in terms of x is x - 0.02x or 0.98x.
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.
The fourth row for the town of Concord would be as follows:
Town | Census Population | Percentage Change
Concord | p | -9%
To write expressions for the current estimated population of Concord in terms of p, we need to calculate the decrease in population by -9% of the previous population.
Expression 1: The first expression can be written as p + (-9% * p), or p - (0.09 * p).
Expression 2: The second expression can be written as p * (1 - 9%), which simplifies to p * (1 - 0.09) or p * 0.91.
So, the two expressions for the current estimated population of Concord in terms of p are:
Expression 1: p - 0.09p = 0.91p
Expression 2: p * 0.91
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.
Let's choose p = 6,500 as the value of p for Concord.
Using expression 1 to calculate the estimated current population of Concord:
Population = p - 0.09p = 0.91p
Population = 0.91 * 6500 = 5,915
Rounded to the nearest whole number, the estimated current population of Concord is 5,915.
I used expression 1 to make this calculation because it directly applies the percentage change (-9%) to the previous population. By subtracting 0.09p from p, we are subtracting 9% of p from p, which represents the decrease in population. This gives us the estimated current population of Concord.