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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 population at the beginning of a particular year be "P".
The population at the end of the year after a 2% increase will be:
P + (2/100)P = P(1 + 0.02) = 1.02P
Similarly, the population at the end of the second year will be:
1.02P + (2/100)(1.02P) = 1.02P(1 + 0.02) = 1.0404P
The population at the end of the third year will be:
1.0404P + (2/100)(1.0404P) = 1.0404P(1 + 0.02) = 1.061208P
We can see that the population is increasing by a factor of 1.02 each year.
Let "n" be the number of years required for the population to increase by 40%.
Using the formula for compound interest:
P(1 + r)^n = P(1 + 0.02)^n = 1.4P
(1.02)^n = 1.4
n = log(1.4) / log(1.02)
n ≈ 35.6
Therefore, it will take approximately 36 years for the population to increase by 40%.
Conclusion: The number of years by which the total increase of population be 40% is approximately 36 years.
Solution:
Let the population at the beginning of a particular year be "P".
The population at the end of the year after a 2% increase will be:
P + (2/100)P = P(1 + 0.02) = 1.02P
Similarly, the population at the end of the second year will be:
1.02P + (2/100)(1.02P) = 1.02P(1 + 0.02) = 1.0404P
The population at the end of the third year will be:
1.0404P + (2/100)(1.0404P) = 1.0404P(1 + 0.02) = 1.061208P
We can see that the population is increasing by a factor of 1.02 each year.
Let "n" be the number of years required for the population to increase by 40%.
Using the formula for compound interest:
P(1 + r)^n = P(1 + 0.02)^n = 1.4P
(1.02)^n = 1.4
n = log(1.4) / log(1.02)
n ≈ 35.6
Therefore, it will take approximately 36 years for the population to increase by 40%.
Conclusion: The number of years by which the total increase of population be 40% is approximately 36 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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