Question 3

Question

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 Population Percentage Change
Pleasantville x –2%
Amity Center y +5%
Harmony Corners z +7%

Choose one of these towns. Use the information from 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.

The population of Pleasantville as of the last census is \( x \), and the population has decreased by 2%. To find the current estimated population, we can use the percentage change.

1. The decrease in population can be calculated as: \[ \text{Decrease} = x \times \left(\frac{-2}{100}\right) = -0.02x \]

2. To find the current estimated population, we subtract the decrease from the last census population: \[ \text{Current Population} = x + (-0.02x) = x - 0.02x = 0.98x \]

So, the two expressions to show the current estimated population for Pleasantville are:

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

Now let’s look at another town, Amity Center.

The population of Amity Center as of the last census is \( y \), and the population has increased by 5%. To find the current estimated population, we can again use the percentage change.

1. The increase in population can be calculated as: \[ \text{Increase} = y \times \left(\frac{5}{100}\right) = 0.05y \]

2. To find the current estimated population, we add the increase to the last census population: \[ \text{Current Population} = y + 0.05y = 1.05y \]

So, the two expressions for Amity Center are:

1. The increase in population: \( 0.05y \)
2. The current estimated population: \( 1.05y \)

Finally, for Harmony Corners:

The population of Harmony Corners as of the last census is \( z \), and the population has increased by 7%.

1. The increase in population can be calculated as: \[ \text{Increase} = z \times \left(\frac{7}{100}\right) = 0.07z \]

2. To find the current estimated population, we add the increase to the last census population: \[ \text{Current Population} = z + 0.07z = 1.07z \]

So, the two expressions for Harmony Corners are:

1. The increase in population: \( 0.07z \)
2. The current estimated population: \( 1.07z \)

In summary, you can use these approaches to calculate the current estimated populations for each town based on their respective changes.

Answer 2

So what's the answer.

Answer 3

Here are the concise answers with expressions for each town:

For Pleasantville:

1. Decrease in population: \( -0.02x \)
2. Current estimated population: \( 0.98x \)

For Amity Center:

1. Increase in population: \( 0.05y \)
2. Current estimated population: \( 1.05y \)

For Harmony Corners:

1. Increase in population: \( 0.07z \)
2. Current estimated population: \( 1.07z \)

You can choose any of the towns (Pleasantville, Amity Center, or Harmony Corners) and use the corresponding expressions for your answer.

Answer 4

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.

Answer 5

Let's add a fourth row for the town of Concord with the following specifications:

• Population as of the last census: \( p \)
• Percentage change: Let's choose a negative integer that is not divisible by two. We'll use \( -3% \).

Updated Table:

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

Expressions for Concord:

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

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

Final Answer for Concord:

1. Decrease in population: \( -0.03p \)
2. Current estimated population: \( 0.97p \)

This provides the necessary information for the town of Concord as requested!