A. Let's choose the town of Pleasantville. We can use the second and third columns to write two expressions showing the current estimated population of Pleasantville in terms of X.

Question

Expression 1: X - 0.02X = X(1 - 0.02) = 0.98X (Since the percentage change is -2%, we subtract 2% or 0.02 from the previous population X.)

Expression 2: X(1 - 2%) = X(1 - 0.02) = 0.98X (This is another way to express the decrease of 2% from the previous population X.)

B. Let's add a fourth row to the table for the town of Concord.

TOWN CENSUS POPULATION PERCENTAGE CHANGE
PLEASANTVILLE X -2%
AMITY CENTER Y +5%
HARMONY CORNERS Z +7%
CONCORD P -3%

We choose a negative integer not divisible by two, -3%, for the percentage change of Concord. Now let's write two expressions showing the current estimated population of Concord in terms of P.

Expression 1: P - 0.03P = P(1 - 0.03) = 0.97P (Since the percentage change is -3%, we subtract 3% or 0.03 from the previous population P.)

Expression 2: P(1 - 3%) = P(1 - 0.03) = 0.97P (This is another way to express the decrease of 3% from the previous population P.)

C. Let's choose P = 7,000 for the value of P. Based on the percentage change of -3% from part B, we can calculate the estimated current population of Concord.

Estimated current population of Concord = 7,000 - 0.03(7,000) = 7,000 - 210 = 6,790 (rounded to the nearest whole number)

We used the expressions 7,000 - 0.03(7,000) and 7,000(1 - 3%) to make the calculation because they represent the decrease of 3% from the previous population of 7,000. The expressions allow us to subtract the percentage decrease from the previous population to get the estimated current population. reword it and make it shorter

Answer 1

A. For the town of Pleasantville, we can express its current estimated population in terms of X as follows:

Expression 1:
X - 0.02X = X(1 - 0.02) = 0.98X
(This shows a 2% decrease from the population X.)

Expression 2:
X(1 - 2%) = X(1 - 0.02) = 0.98X
(This is another way to indicate the 2% decrease.)

B. Now let's add a row for Concord:

| TOWN | CENSUS | POPULATION | PERCENTAGE CHANGE | |-------------------|--------|------------|--------------------| | PLEASANTVILLE | X | | -2% | | AMITY CENTER | Y | | +5% | | HARMONY CORNERS | Z | | +7% | | CONCORD | P | | -3% |

For Concord, with a percentage change of -3%, we can write:

Expression 1:
P - 0.03P = P(1 - 0.03) = 0.97P
(This represents a 3% decrease from population P.)

Expression 2:
P(1 - 3%) = P(1 - 0.03) = 0.97P
(This also shows the 3% decrease.)

C. Let’s set P = 7,000. The estimated current population of Concord is:

Estimated current population = 7,000 - 0.03(7,000) = 7,000 - 210 = 6,790.

We used the expressions 7,000 - 0.03(7,000) and 7,000(1 - 3%) to calculate this, as they both reflect the 3% decrease from the previous population.