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The population of a town increase every year by 2% of the population at the beginning of that year the number of year by which the total increase of population b 40% is?
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The population of a town increase every year by 2% of the population a...
Population Growth Calculation
- Let's assume the population of the town at the beginning of the year is P.
- The population increases by 2% of P every year.
- So, the population at the end of the first year will be P + 0.02P = 1.02P.
- Similarly, the population at the end of the second year will be 1.02P + 0.02(1.02P) = 1.02P(1 + 0.02) = 1.02^2P.
- In general, the population at the end of n years will be P(1.02)^n.
Calculating the Total Increase
- To find the number of years by which the total increase of the population is 40%, we need to solve the equation:
- P(1.02)^n - P = 0.4P
- Simplifying this equation, we get:
- (1.02)^n = 1.4
- Taking the natural logarithm of both sides:
- n * ln(1.02) = ln(1.4)
- n = ln(1.4) / ln(1.02)
- n ≈ 35.002
Explanation
- Therefore, it will take approximately 35 years for the total increase in population to reach 40%.
- This calculation is based on the assumption that the population growth rate remains constant at 2% per year.
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The population of a town increase every year by 2% of the population at the beginning of that year the number of year by which the total increase of population b 40% is?
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The population of a town increase every year by 2% of the population at the beginning of that year the number of year by which the total increase of population b 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 increase every year by 2% of the population at the beginning of that year the number of year by which the total increase of population b 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 increase every year by 2% of the population at the beginning of that year the number of year by which the total increase of population b 40% is?.
The population of a town increase every year by 2% of the population at the beginning of that year the number of year by which the total increase of population b 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 increase every year by 2% of the population at the beginning of that year the number of year by which the total increase of population b 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 increase every year by 2% of the population at the beginning of that year the number of year by which the total increase of population b 40% is?.
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