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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
- a)7 years
- b)10 years
- c)17 years
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The population of a town increases every year by 2% of the population ...
To determine the number of years it takes for the population to increase by 40% given a 2% annual increase, we can use the compound interest formula:
Thus, the number of years it takes for the population to increase by 40% is approximately 17 years.
Most Upvoted Answer
The population of a town increases every year by 2% of the population ...
Given:
- Population increases every year by 2% of the population at the beginning of that year.
- Total increase of population is 40%.
To find:
- Number of years it takes for the population to increase by 40%.
Solution:
Let the initial population be P.
After 1 year, the population increases by 2% of P, which is 0.02P.
So, after the first year, the population becomes P + 0.02P = 1.02P.
Similarly, after 2 years, the population becomes 1.02P + 0.02(1.02P) = 1.0404P.
In general, after n years, the population becomes:
P(1 + 0.02)n
We want to find the number of years it takes for the population to increase by 40%.
So, we want to solve the equation:
P(1 + 0.02)n - P = 0.4P
Simplifying and solving for n, we get:
(1 + 0.02)n - 1 = 0.4/1.02
Using a calculator or trial and error, we find that n is approximately 17.
Therefore, it takes 17 years for the population to increase by 40%.
Answer: (c) 17 years
- Population increases every year by 2% of the population at the beginning of that year.
- Total increase of population is 40%.
To find:
- Number of years it takes for the population to increase by 40%.
Solution:
Let the initial population be P.
After 1 year, the population increases by 2% of P, which is 0.02P.
So, after the first year, the population becomes P + 0.02P = 1.02P.
Similarly, after 2 years, the population becomes 1.02P + 0.02(1.02P) = 1.0404P.
In general, after n years, the population becomes:
P(1 + 0.02)n
We want to find the number of years it takes for the population to increase by 40%.
So, we want to solve the equation:
P(1 + 0.02)n - P = 0.4P
Simplifying and solving for n, we get:
(1 + 0.02)n - 1 = 0.4/1.02
Using a calculator or trial and error, we find that n is approximately 17.
Therefore, it takes 17 years for the population to increase by 40%.
Answer: (c) 17 years
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Community Answer
The population of a town increases every year by 2% of the population ...
A=1.4P
P(1.02)n=1.4P
(1.02)n = 1.4
n=17
P(1.02)n=1.4P
(1.02)n = 1.4
n=17
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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% isa)7 yearsb)10 yearsc)17 yearsd)none of theseCorrect answer is option 'C'. Can you explain this answer?
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