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.

Question

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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Answer 1

To answer your questions:

3a. To calculate the estimated population given a percentage increase or decrease in population, we can use the following expression:

• Let \( y \) represent the population from the last census.
• If there is an estimated decrease of 5%, for example, you would decrease the population by 5% of \( y \). This can be expressed as:

\[ y - (y \times 0.05) \]

Therefore, the correct response would be:

y - (y x 0.05)

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3b. If the previous census showed 6,500 people living in Harmony Corners and there is a percentage decrease given in the chart, we will apply the percentage change to calculate the current population. For example, if the percentage decrease from the census is 30%, you would compute it as follows:

1. Calculate 30% of 6,500: \[ 0.30 \times 6,500 = 1,950 \]

2. Subtract that value from the census population: \[ 6,500 - 1,950 = 4,550 \]

Hence, if the percentage change for Harmony Corners indicates a decrease of 30%, the estimated current population would be:

4,550 people

If the decrease percentage is different, simply adjust the calculations accordingly. Based on the options provided and assuming a 30% decrease, 4,550 is indeed the estimated current population.