Question 1

Question

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 (A census is a count of people that live in a specific place). The third column gives the estimated increase or decrease in population since that census, expressed as a percentage of the previous population.

3a. Ella wants to write an expression to figure out the estimated population in the town of Amity Center. Which expression could she use to figure this out?

(2 points)
Responses

y + 5
y + 5

y + (y x 0.05)
y + (y x 0.05)

y - (y x 0.05)
y - (y x 0.05)

y - 5
y - 5
Question 2






3b. Based on the percentage change in the chart above, calculate the estimated current population of Harmony Corners if the previous census showed 6,500 people living in that town.

(3 points)
Responses

4,550 people
4,550 people

6,507 people
6,507 people

6,955 people
6,955 people

11,050 people
11,050 people
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page 15 of 15

Answer 1

To answer your questions, let's break them down one by one.

Question 3a

Ella wants to write an expression to figure out the estimated population in the town of Amity Center. If Amity Center's population changes by a percentage (for example, an increase or decrease of 5%), the population can be expressed in terms of the original population (let's denote the original population as \( y \)) as follows:

• If the population increases by 5%, you would compute it as: \[ y + (y \times 0.05) = y(1 + 0.05) = y \times 1.05 \]

• If the population decreases by 5%, you would compute it as: \[ y - (y \times 0.05) = y(1 - 0.05) = y \times 0.95 \]

Assuming the percentage change for Amity Center is a decrease of 5%, the correct expression based on the options provided would be: \( y - (y \times 0.05) \).

So, the correct response for this question is:

• y - (y x 0.05)

Question 3b

For the town of Harmony Corners, if the last census showed a population of 6,500 and assuming the percentage change is a decrease (as is common in these types of problems), we need to find out the percentage given in the chart you mentioned (not provided here). Assuming we follow the same trend of a decrease of 5%, we calculate the estimated current population as follows:

1. Calculate the decrease: \[ 6,500 \times 0.05 = 325 \]

2. Subtract the decrease from the original population: \[ 6,500 - 325 = 6,175 \]

However, this number is not one of your options. If Harmony Corners is assuming a different percentage decrease, you would apply that percentage using the same method.

Please provide the percentage change for Harmony Corners if different from 5% so we can calculate the correct estimated current population.

If we assume it is a 5% decrease based on common percentages, the response for the estimated population is not available in the options you provided. If it were less than 6,500, the possible option closest would need to be verified with the correct percentage. Could you please share that?