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The annual birth and death rates per 1000 are 39.4 and 19.4 respectively. The number of years in which the population will be doubled assuming there is no immigration or emigration is
- a)35 yrs.
- b)30 yrs.
- c)25 yrs
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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The annual birth and death rates per 1000 are 39.4 and 19.4 respective...
Given data:
Annual birth rate = 39.4 per 1000
Annual death rate = 19.4 per 1000
We need to find the number of years in which the population will be doubled.
Formula used:
Population after n years = Initial population x (1 + r/100)^n
where r = (birth rate - death rate)
Assuming that there is no immigration or emigration, the net growth rate (r) can be calculated as:
r = (birth rate - death rate) = (39.4 - 19.4) = 20
Calculation:
Let P be the initial population
Population after 1 year = P x (1 + 20/100) = 1.2P
Population after 2 years = 1.2P x (1 + 20/100) = 1.44P
Population after 3 years = 1.44P x (1 + 20/100) = 1.728P
...
Population after n years = P x (1 + 20/100)^n
We need to find the number of years (n) in which the population will be doubled, i.e., 2P = P x (1 + 20/100)^n
Simplifying this equation, we get:
2 = (1 + 20/100)^n
Taking log on both sides, we get:
n x log(1.2) = log(2)
n = log(2)/log(1.2) ≈ 35 years (rounded to nearest integer)
Therefore, the number of years in which the population will be doubled assuming there is no immigration or emigration is 35 years.
Annual birth rate = 39.4 per 1000
Annual death rate = 19.4 per 1000
We need to find the number of years in which the population will be doubled.
Formula used:
Population after n years = Initial population x (1 + r/100)^n
where r = (birth rate - death rate)
Assuming that there is no immigration or emigration, the net growth rate (r) can be calculated as:
r = (birth rate - death rate) = (39.4 - 19.4) = 20
Calculation:
Let P be the initial population
Population after 1 year = P x (1 + 20/100) = 1.2P
Population after 2 years = 1.2P x (1 + 20/100) = 1.44P
Population after 3 years = 1.44P x (1 + 20/100) = 1.728P
...
Population after n years = P x (1 + 20/100)^n
We need to find the number of years (n) in which the population will be doubled, i.e., 2P = P x (1 + 20/100)^n
Simplifying this equation, we get:
2 = (1 + 20/100)^n
Taking log on both sides, we get:
n x log(1.2) = log(2)
n = log(2)/log(1.2) ≈ 35 years (rounded to nearest integer)
Therefore, the number of years in which the population will be doubled assuming there is no immigration or emigration is 35 years.
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The annual birth and death rates per 1000 are 39.4 and 19.4 respective...
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The annual birth and death rates per 1000 are 39.4 and 19.4 respectively. The number of years in which the population will be doubled assuming there is no immigration or emigration isa)35 yrs.b)30 yrs.c)25 yrsd)None of theseCorrect answer is option 'A'. Can you explain this answer?
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