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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?
Most Upvoted Answer
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.
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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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