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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?
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The population of a town increases every year by 2% of the population ...
Problem: 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?
Solution:
Let the initial population of the town be P.
At the end of the 1st year, the population will be P + 2% of P = P(1 + 2/100) = P(1.02)
At the end of the 2nd year, the population will be P(1.02) + 2% of P(1.02) = P(1.02)^2
Similarly, at the end of the n-th year, the population will be P(1.02)^n
Therefore, we need to find the value of n such that P(1.02)^n - P = 0.4P
Simplifying this equation, we get (1.02)^n = 1.4
Taking the logarithm of both sides, we get n log(1.02) = log(1.4)
Therefore, n = log(1.4) / log(1.02) ≈ 35.2 years
Hence, the number of years by which the total increase of population will be 40% is approximately 35.2 years.
Answer: The number of years by which the total increase of population will be 40% is approximately 35.2 years.
Solution:
Let the initial population of the town be P.
At the end of the 1st year, the population will be P + 2% of P = P(1 + 2/100) = P(1.02)
At the end of the 2nd year, the population will be P(1.02) + 2% of P(1.02) = P(1.02)^2
Similarly, at the end of the n-th year, the population will be P(1.02)^n
Therefore, we need to find the value of n such that P(1.02)^n - P = 0.4P
Simplifying this equation, we get (1.02)^n = 1.4
Taking the logarithm of both sides, we get n log(1.02) = log(1.4)
Therefore, n = log(1.4) / log(1.02) ≈ 35.2 years
Hence, the number of years by which the total increase of population will be 40% is approximately 35.2 years.
Answer: The number of years by which the total increase of population will be 40% is approximately 35.2 years.
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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?
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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? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 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? covers all topics & solutions for CA Foundation 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 at the beginning of that year. The 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 at the beginning of that year. The number of years by which the total increase of population be 40% is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 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? covers all topics & solutions for CA Foundation 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 at the beginning of that year. The number of years by which the total increase of population be 40% is?.
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