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Boomtown urban planners expect the city’s population to increase by 10
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17 Mar 2021, 03:02
17 Mar 2021, 03:02
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Boomtown urban planners expect the city’s population to increase by 10% per year over the next two years. If that projection were to come true, the population two years from now would be exactly double the population of one year ago. Which of the following is closest to the percent population increase in Boomtown over the last year?
A. 20%
B. 40%
C. 50%
D. 65%
E. 75%
A. 20%
B. 40%
C. 50%
D. 65%
E. 75%
Re: Boomtown urban planners expect the city’s population to increase by 10
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17 Mar 2021, 08:25
17 Mar 2021, 08:25
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Let's take the current population of city = 10000
10% increase every year
Next year population = 11000
After one year population = 1.10 * 11000 = 12100
Now it is given that the population two years from now would be exactly double the population of one year ago.
So 12100 is double the population of last year.
Population of the last year will be \(\frac{12100}{2}\) = 6050
Now %age increase = \(\frac{current_population}{last_year's_population}\) = \(\frac{10000}{6050}\) = 65.28%
Answer D
10% increase every year
Next year population = 11000
After one year population = 1.10 * 11000 = 12100
Now it is given that the population two years from now would be exactly double the population of one year ago.
So 12100 is double the population of last year.
Population of the last year will be \(\frac{12100}{2}\) = 6050
Now %age increase = \(\frac{current_population}{last_year's_population}\) = \(\frac{10000}{6050}\) = 65.28%
Answer D
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Re: Boomtown urban planners expect the city’s population to increase by 10
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17 Mar 2021, 09:22
17 Mar 2021, 09:22
GeminiHeat wrote:
Boomtown urban planners expect the city’s population to increase by 10% per year over the next two years. If that projection were to come true, the population two years from now would be exactly double the population of one year ago. Which of the following is closest to the percent population increase in Boomtown over the last year?
A. 20%
B. 40%
C. 50%
D. 65%
E. 75%
A. 20%
B. 40%
C. 50%
D. 65%
E. 75%
Let,
Last year population be \(y\), and
This year population be \(x\)
Population after 2 years = \((1.1)(1.1)(x) = 1.21x\)
As per the question, \(1.21x = 2y\) i.e. \(y = 0.605x\)
Now percent change = \(\frac{(x - 0.605x)}{0.605x}(100) = 65.28\)%
Hence, option D
