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The population of a town increases every year by 2% of the population beginning of that year.T he number of years by which the total increase of population be 40% is?
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The population of a town increases every year by 2% of the population ...
Understanding the Problem
The population of a town increases by 2% every year, and we need to find out the number of years it takes for the total increase in population to reach 40%.
Solution
- Let's assume the initial population of the town is P.
- After the first year, the population will be P + 0.02P = 1.02P.
- After the second year, it will be 1.02P + 0.02(1.02P) = 1.02P(1 + 0.02) = 1.02P(1.02).
- Similarly, after n years, the population will be P(1.02)^n.
- We need to find the number of years it takes for the population to increase by 40%.
- The total increase will be 0.4P.
- So, we set up the equation: P(1.02)^n - P = 0.4P.
- Simplifying, we get (1.02)^n - 1 = 0.4.
- Solving for n, we find n = log(1.4) / log(1.02) ≈ 35.7 years.
Therefore, it will take approximately 36 years for the total increase in population to reach 40%.
The population of a town increases by 2% every year, and we need to find out the number of years it takes for the total increase in population to reach 40%.
Solution
- Let's assume the initial population of the town is P.
- After the first year, the population will be P + 0.02P = 1.02P.
- After the second year, it will be 1.02P + 0.02(1.02P) = 1.02P(1 + 0.02) = 1.02P(1.02).
- Similarly, after n years, the population will be P(1.02)^n.
- We need to find the number of years it takes for the population to increase by 40%.
- The total increase will be 0.4P.
- So, we set up the equation: P(1.02)^n - P = 0.4P.
- Simplifying, we get (1.02)^n - 1 = 0.4.
- Solving for n, we find n = log(1.4) / log(1.02) ≈ 35.7 years.
Therefore, it will take approximately 36 years for the total increase in population to reach 40%.
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The population of a town increases every year by 2% of the population beginning of that year.T he number of years by which the total increase of population be 40% is?
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The population of a town increases every year by 2% of the population beginning of that year.T he number of years by which the total increase of population be 40% is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The population of a town increases every year by 2% of the population beginning of that year.T he number of years by which the total increase of population be 40% is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The population of a town increases every year by 2% of the population beginning of that year.T he number of years by which the total increase of population be 40% is?.
The population of a town increases every year by 2% of the population beginning of that year.T he number of years by which the total increase of population be 40% is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The population of a town increases every year by 2% of the population beginning of that year.T he number of years by which the total increase of population be 40% is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The population of a town increases every year by 2% of the population beginning of that year.T he number of years by which the total increase of population be 40% is?.
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