Four different towns in the same state grew in size due to a renewal effort. The population of town A grew from 22,000 to 24,500 in 4 years. The population of town B grew from 31,200 to 34,770 in 6 years. The population of town C grew from 18,000 to 22,000 in 5 years. The population of town D grew from 32,000 to 34,100 in 3 years. Which town had the greatest average change in population over the corresponding time period?(1 point)
Responses
town B
town B
town D
town D
town A
town A
town C
town B
To determine which town had the greatest average change in population over the corresponding time period, we need to calculate the average change in population for each town.
The average change in population can be calculated by subtracting the initial population from the final population, and then dividing that difference by the number of years.
For town A:
Initial population = 22,000
Final population = 24,500
Number of years = 4
Average change in population = (Final population - Initial population) / Number of years
Average change in population = (24,500 - 22,000) / 4
Average change in population = 2,500 / 4
Average change in population = 625
For town B:
Initial population = 31,200
Final population = 34,770
Number of years = 6
Average change in population = (Final population - Initial population) / Number of years
Average change in population = (34,770 - 31,200) / 6
Average change in population = 3,570 / 6
Average change in population = 595
For town C:
Initial population = 18,000
Final population = 22,000
Number of years = 5
Average change in population = (Final population - Initial population) / Number of years
Average change in population = (22,000 - 18,000) / 5
Average change in population = 4,000 / 5
Average change in population = 800
For town D:
Initial population = 32,000
Final population = 34,100
Number of years = 3
Average change in population = (Final population - Initial population) / Number of years
Average change in population = (34,100 - 32,000) / 3
Average change in population = 2,100 / 3
Average change in population = 700
Based on the calculations above, town C had the greatest average change in population over the corresponding time period, with an average change of 800.
To find the average change in population for each town, we need to calculate the change in population over the corresponding time period and then divide that change by the number of years.
For town A:
Change in population = 24,500 - 22,000 = 2,500
Average change = 2,500 / 4 = 625
For town B:
Change in population = 34,770 - 31,200 = 3,570
Average change = 3,570 / 6 = 595
For town C:
Change in population = 22,000 - 18,000 = 4,000
Average change = 4,000 / 5 = 800
For town D:
Change in population = 34,100 - 32,000 = 2,100
Average change = 2,100 / 3 = 700
Comparing the average changes, we can see that town C had the greatest average change in population over the corresponding time period of 5 years. Therefore, the correct answer is town C.