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Question
The population of Bigville increased from 387,480 to 571,533 in the last 7 years. During the same time period, Smallville increased its population by 53.67%. Compare the towns to determine which is growing at the greatest rate and by what factor? (round to nearest hundredth)
Responses
A Bigville by a factor of 1.13Bigville by a factor of 1.13
B Bigville by a factor of 6.17Bigville by a factor of 6.17
C Smallville by a factor of 1.13Smallville by a factor of 1.13
D Smallville by a factor of 6.17Smallville by a factor of 6.17
To determine which town is growing at the greatest rate and by what factor, we need to calculate the percentage increase for each town.
The percentage increase for Bigville can be calculated by finding the difference between the final population (571,533) and the initial population (387,480), and then dividing that difference by the initial population and multiplying by 100:
((571,533 - 387,480) / 387,480) * 100 = 47.57%
So, Bigville increased its population by 47.57%.
The percentage increase for Smallville is given as 53.67%.
Comparing the percentage increases, we can see that Smallville had a higher percentage increase (53.67% compared to 47.57%). Therefore, Smallville is growing at a greater rate than Bigville.
To determine the factor by which each town is growing, we can calculate the multiplier for each percentage increase:
For Bigville, the multiplier is given by (100% + 47.57%) / 100% = 1 + 0.4757 = 1.4757.
For Smallville, the multiplier is given by (100% + 53.67%) / 100% = 1 + 0.5367 = 1.5367.
Rounding to the nearest hundredth, we find that Bigville is growing by a factor of 1.48, and Smallville is growing by a factor of 1.54.
Therefore, the correct answer is:
C. Smallville by a factor of 1.13