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The population of a town increases every year by 2 % of the population 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 (approximately)
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The population of a town increases every year by 2 % of the population...
Let the population (P) be 100
Total increase (A) be 100+40 = 140
i = 0.02. n=?
A = P (1+i)^n
140 = 100 ( 1+0.02)^n
140/100 = (1.02)^n
1.4 = (1.02)^n
Taking log on both sides
log 1.4 = n. log (1.02)
n = log 1.4 ÷ log 1.02
n = 0.1461 ÷ 0.0086
n = 16.988 ~ 17 years (approx)
Total increase (A) be 100+40 = 140
i = 0.02. n=?
A = P (1+i)^n
140 = 100 ( 1+0.02)^n
140/100 = (1.02)^n
1.4 = (1.02)^n
Taking log on both sides
log 1.4 = n. log (1.02)
n = log 1.4 ÷ log 1.02
n = 0.1461 ÷ 0.0086
n = 16.988 ~ 17 years (approx)
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The population of a town increases every year by 2 % of the population...
Given:
- Population of a town increases every year by 2% of the population beginning of that year
- Total increase of population is 40%
To find: Number of years by which the total increase of population be 40%
Solution:
Let the population at the beginning of the year be P.
After one year, the population will be P + 2% of P = 1.02P
After two years, the population will be 1.02P + 2% of 1.02P = 1.0404P
After three years, the population will be 1.0404P + 2% of 1.0404P = 1.061208P
After n years, the population will be P(1.02)^n
Given that the total increase of population is 40%, we have:
P(1.02)^n - P = 0.4P
Simplifying this equation, we get:
(1.02)^n = 1.4
Taking logarithm on both sides, we get:
n log(1.02) = log(1.4)
n = log(1.4) / log(1.02)
Using a calculator, we get:
n = 16.99
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.
- Population of a town increases every year by 2% of the population beginning of that year
- Total increase of population is 40%
To find: Number of years by which the total increase of population be 40%
Solution:
Let the population at the beginning of the year be P.
After one year, the population will be P + 2% of P = 1.02P
After two years, the population will be 1.02P + 2% of 1.02P = 1.0404P
After three years, the population will be 1.0404P + 2% of 1.0404P = 1.061208P
After n years, the population will be P(1.02)^n
Given that the total increase of population is 40%, we have:
P(1.02)^n - P = 0.4P
Simplifying this equation, we get:
(1.02)^n = 1.4
Taking logarithm on both sides, we get:
n log(1.02) = log(1.4)
n = log(1.4) / log(1.02)
Using a calculator, we get:
n = 16.99
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 beginning of that year. The number of years by which the total increase of population be 40% isa)7 yearsb)10 yearsc)17 years (approximately)d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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