Question 3 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 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.n make it short write like a 4 th grader

Answer 1

Let's pick Pleasantville!

The last census showed that the population was x. Since it decreased by 2%, we can find the current population like this:

1. Current Population of Pleasantville: \( \text{Current Population} = x - 0.02x = 0.98x \)

Now, let's look at a different town, Amity Center.

The last census showed that the population was y. Since it increased by 5%, we can find the current population like this:

2. Current Population of Amity Center: \( \text{Current Population} = y + 0.05y = 1.05y \)

So, for Pleasantville, the current estimated population is 0.98x, and for Amity Center, it's 1.05y!

Answer 2

and dont choose a random number for x y or z just use (example) x - 0.02 = total

Answer 3

Sure! Let's keep it simple using the letters x, y, and z without choosing random numbers.

For Pleasantville, the current estimated population is:

1. Pleasantville:
   \( \text{Current Population} = x - 0.02x = 0.98x \)
   or
   \( \text{Current Population} = x(1 - 0.02) \)

For Amity Center, the current estimated population is:

2. Amity Center:
   \( \text{Current Population} = y + 0.05y = 1.05y \)
   or
   \( \text{Current Population} = y(1 + 0.05) \)

And for Harmony Corners, the current estimated population is:

3. Harmony Corners:
   \( \text{Current Population} = z + 0.07z = 1.07z \)
   or
   \( \text{Current Population} = z(1 + 0.07) \)

So, the expressions for the populations are:

• Pleasantville: \( 0.98x \) or \( x(1 - 0.02) \)
• Amity Center: \( 1.05y \) or \( y(1 + 0.05) \)
• Harmony Corners: \( 1.07z \) or \( z(1 + 0.07) \)

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

Sure! Let's add a fourth row for the town of Concord, with a negative percentage change. Let's say Concord's population decreased by 3%.

Here’s the updated table with Concord included:

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

For Concord, the current estimated population can be expressed as:

1. Current Population of Concord:
   \( \text{Current Population} = p - 0.03p = 0.97p \)
   or
   \( \text{Current Population} = p(1 - 0.03) \)

So, the expressions for Concord are:

• \( 0.97p \)
• \( p(1 - 0.03) \)

This shows the current estimated population of Concord in terms of \( p \).

Answer 6

stop doing = random number do = total THE WORD TOTAL

Answer 7

Got it! I'll use "total" to indicate the current estimated population. Let's write it correctly this time for Concord.

For the town of Concord, where the population as of the last census was p and it decreased by 3%, the expressions showing the current estimated population would be:

1. Total Current Population of Concord:
   \( \text{Total} = p - 0.03p = 0.97p \)
   or
   \( \text{Total} = p(1 - 0.03) \)

So, for Concord, you can say:

• Total = \( 0.97p \)
• Total = \( p(1 - 0.03) \)

Thank you for your patience!

Answer 8

YOUR STILL DOING IT MAKE = 0.97P THE WORD TOTAL

Answer 9

I apologize for misunderstanding your request. Let’s use “Total” explicitly as you asked. Here’s the information correctly formatted:

For the town of Concord, where the population as of the last census was p and it decreased by 3%, the expressions showing the current estimated population are:

1. Total = \( p - 0.03p \)
2. Total = \( p(1 - 0.03) \)

So for Concord:

• Total = \( 0.97p \)
• Total = \( p(1 - 0.03) \)

Thank you for your guidance!

Answer 10

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. im choosing p = 7000 and the percentage i choose is - 3%

Answer 11

Great choice! Let's use \( p = 7000 \) and a percentage change of -3% to calculate the estimated current population of Concord.

Calculation

1. Find the expression for the current population: Since the population decreased by 3%, we can use the expression: \[ \text{Total} = p(1 - 0.03) \]

2. Substitute \( p = 7000 \) into the expression: \[ \text{Total} = 7000(1 - 0.03) = 7000(0.97) \]

3. Calculate: \[ \text{Total} = 7000 \times 0.97 = 6790 \]

So, the estimated current population of Concord is 6790.

Explanation

I used the expression \( \text{Total} = p(1 - 0.03) \) because it accurately reflects the percentage change in population. Since we know the population decreased by 3%, we multiply the original population, \( p \), by \( (1 - 0.03) \) to account for that decrease. This calculation gives us the current estimated population after the decrease is applied. Rounding is not necessary in this case since 6790 is already a whole number.