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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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Verified Answer
The annual birth and death rates per 1000 are 39.4 and 19.4 respective...
Given: b( birth rate)=39.4/1000, d(death rate) =19.4/1000
b-d= 39.4–19.4=20/1000 i.e.0.02
P( population) = 2P( population)
To find: t=?
Solution :Let's assume P=1000
applying formula:
An= p(1+i)n
Putting values:
2000=1000(1+0.02)n
2=1.02n
n=35 years.
Most Upvoted Answer
The annual birth and death rates per 1000 are 39.4 and 19.4 respective...
Solution:
Given:
- Annual birth rate = 39.4 per 1000
- Annual death rate = 19.4 per 1000
Let the current population be P.
After one year, the population will be:
P + (39.4/1000)P - (19.4/1000)P = 1.2P
After two years, the population will be:
1.2P + (39.4/1000)(1.2P) - (19.4/1000)(1.2P) = 1.44P
Similarly, after three years, the population will be:
1.44P + (39.4/1000)(1.44P) - (19.4/1000)(1.44P) = 1.728P
After n years, the population will be:
P(1 + 0.02)n
To find the number of years it takes for the population to double, we need to solve the following equation:
2P = P(1 + 0.02)n
Simplifying, we get:
2 = 1.02n
Taking the logarithm of both sides, we get:
n = log(2)/log(1.02)
n ≈ 35
Therefore, the number of years it takes for the population to double is 35 years.
Hence, option (a) is the correct answer.
Given:
- Annual birth rate = 39.4 per 1000
- Annual death rate = 19.4 per 1000
Let the current population be P.
After one year, the population will be:
P + (39.4/1000)P - (19.4/1000)P = 1.2P
After two years, the population will be:
1.2P + (39.4/1000)(1.2P) - (19.4/1000)(1.2P) = 1.44P
Similarly, after three years, the population will be:
1.44P + (39.4/1000)(1.44P) - (19.4/1000)(1.44P) = 1.728P
After n years, the population will be:
P(1 + 0.02)n
To find the number of years it takes for the population to double, we need to solve the following equation:
2P = P(1 + 0.02)n
Simplifying, we get:
2 = 1.02n
Taking the logarithm of both sides, we get:
n = log(2)/log(1.02)
n ≈ 35
Therefore, the number of years it takes for the population to double is 35 years.
Hence, option (a) is the correct answer.
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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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