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%
Based on the given information, the population trends in the three local towns are as follows:
- Pleasantville: The population decreased by 2% since the last census.
- Amity Center: The population increased by 5% since the last census.
- Harmony Corners: The population increased by 7% since the last census.
. 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 Pleasantville.
The current estimated population of Pleasantville can be expressed using the second column as:
Population of Pleasantville = x + (-2% of x) = x - 0.02x = 0.98x
Therefore, the current estimated population of Pleasantville in terms of x is 0.98x.
To find the population change in each town, we need to use the information provided in the last two columns of the table: the population as of the last census and the percentage change in population.
For Pleasantville, the population change is given as -2% of the previous population. To calculate this, we need to multiply the previous population by 0.02 (since -2% is equivalent to -0.02 as a decimal). The resulting value will be subtracted from the previous population.
Mathematically, the population change in Pleasantville can be calculated as:
Population Change = Previous Population * (Percentage Change / 100)
Population Change = x * (-2 / 100) = -0.02x
For Amity Center, the population change is given as +5% of the previous population. To calculate this, we need to multiply the previous population by 0.05 (since +5% is equivalent to 0.05 as a decimal). The resulting value will be added to the previous population.
Mathematically, the population change in Amity Center can be calculated as:
Population Change = Previous Population * (Percentage Change / 100)
Population Change = y * (5 / 100) = 0.05y
For Harmony Corners, the population change is given as +7% of the previous population. To calculate this, we need to multiply the previous population by 0.07 (since +7% is equivalent to 0.07 as a decimal). The resulting value will be added to the previous population.
Mathematically, the population change in Harmony Corners can be calculated as:
Population Change = Previous Population * (Percentage Change / 100)
Population Change = z * (7 / 100) = 0.07z
In summary:
- The population change in Pleasantville is -0.02x.
- The population change in Amity Center is 0.05y.
- The population change in Harmony Corners is 0.07z.