A county planner prepares the following table showing population trends in three local

Question

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%
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.

Answer 1

Let's choose Pleasantville for this example.

1. The population as of the last census is \( x \).
2. The percentage change in population is \(-2%\).

To find the current estimated population of Pleasantville, we start by calculating the decrease in population based on the percentage change.

The expression for the decrease in population is:

\[ \text{Decrease} = \frac{-2}{100} \times x = -0.02x \]

Now, we can express the current estimated population by subtracting this decrease from the original population:

\[ \text{Current Population of Pleasantville} = x + (-0.02x) = x - 0.02x = 0.98x \]

So, the two expressions showing the current estimated population of Pleasantville are:

1. The decrease in population: \(-0.02x\)
2. The current estimated population: \(0.98x\)

Answer 2

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. keep answer short

Answer 3

Let's say Concord's percentage change is \(-3%\).

Here’s the updated table:

| Town | Census Population | Percentage Change | |-------------------|------------------|-------------------| | Pleasantville | x | -2% | | Amity Center | y | +5% | | Harmony Corners | z | +7% | | Concord | p | -3% |

Expressions for Concord:

1. Decrease in population: \[ \text{Decrease} = \frac{-3}{100} \times p = -0.03p \]

2. Current estimated population: \[ \text{Current Population of Concord} = p + (-0.03p) = 0.97p \]

Answer 4

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. keep answer short

Answer 5

Let's choose \( p = 7,500 \) for the value of Concord's population.

Calculation:

1. The percentage change for Concord is \(-3%\).
2. Using the expression for the current estimated population: \[ \text{Current Population} = 0.97p \]
3. Substitute \( p = 7,500 \): \[ \text{Current Population} = 0.97 \times 7,500 = 7,275 \]

Explanation:

I used the expression \( 0.97p \) because it accounts for the decrease in population due to the \(-3%\) change. This percentage change shows that Concord's population decreased, and multiplying the original population \( p \) by \( 0.97 \) reflects this decrease accurately. Thus, the estimated current population is approximately 7,275.