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%
a. 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.
Let's choose the town Amity Center.
The expression showing the current estimated population of Amity Center in terms of y would be:
Current population of Amity Center = y + 5% of y
The expression showing the current estimated population of Amity Center in terms of x would be:
Current population of Amity Center = x + 5% of x
no, harmony corner
Apologies for the confusion. Let's choose the town Harmony Corners.
The expression showing the current estimated population of Harmony Corners in terms of z would be:
Current population of Harmony Corners = z + 7% of z
Alternatively, we can write it as:
Current population of Harmony Corners = z + 0.07z
Both expressions represent the current estimated population of Harmony Corners based on the given percentage change.
To write two expressions showing the current estimated population of a town in terms of x, y, or z using the second and third columns, we can use the following approach:
1. Start with the population from the last census (x, y, or z).
2. Apply the percentage change to that population.
For example, let's choose the town Pleasantville with a population at the last census of x and a decrease of 2%.
Expression 1:
To find the current estimated population, we need to calculate the decrease and subtract it from the population at the last census.
Decrease = 2% * x
Current estimated population of Pleasantville = x - (2% * x) = x - (0.02 * x) = x - 0.02x = 0.98x
Therefore, the first expression for the current estimated population of Pleasantville in terms of x is: 0.98x.
Expression 2:
Another way to express the current estimated population is by considering the decrease as a negative change and subtracting it from the population at the last census.
Current estimated population of Pleasantville = x + (-2% * x) = x + (-0.02 * x) = x - 0.02x = 0.98x
Thus, the second expression for the current estimated population of Pleasantville in terms of x is also: 0.98x.
Note: The same approach can be applied to the other towns (Amity Center and Harmony Corners) for their respective population estimates using the given percentage changes (y + 5% and z + 7%).