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The population of a town increases every year by 2% of the population at the beginning of that year. The number of years by which the total increase of population be 40% is
- a)7 years
- b)10 years
- c)17 years (app)
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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The population of a town increases every year by 2% of the population ...
Solution:
Let the population of the town at the beginning of the year be x.
Given, the population of the town increases by 2% every year.
After n years, the population of the town will be
x(1+2/100)^n = x(1.02)^n
Total increase in population after n years = x(1.02)^n - x
According to the question, the total increase in population after some years should be 40% of the population at the beginning of the year.
i.e., x(1.02)^n - x = 40/100 * x
Simplifying the above equation, we get
(1.02)^n = 1.4
Taking the logarithm on both sides, we get
n*log(1.02) = log(1.4)
n = log(1.4)/log(1.02)
n = 17.67 (approx)
Therefore, the number of years by which the total increase of population be 40% is approximately 17 years.
Hence, option (c) is the correct answer.
Let the population of the town at the beginning of the year be x.
Given, the population of the town increases by 2% every year.
After n years, the population of the town will be
x(1+2/100)^n = x(1.02)^n
Total increase in population after n years = x(1.02)^n - x
According to the question, the total increase in population after some years should be 40% of the population at the beginning of the year.
i.e., x(1.02)^n - x = 40/100 * x
Simplifying the above equation, we get
(1.02)^n = 1.4
Taking the logarithm on both sides, we get
n*log(1.02) = log(1.4)
n = log(1.4)/log(1.02)
n = 17.67 (approx)
Therefore, the number of years by which the total increase of population be 40% is approximately 17 years.
Hence, option (c) is the correct answer.
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The population of a town increases every year by 2% of the population at the beginning of that year. The number of years by which the total increase of population be 40% isa)7 yearsb)10 yearsc)17 years (app)d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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