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The annual birth and death rates per 1,000 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 years. (b) 30 years. (c) 25 years (d) none of these?
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The annual birth and death rates per 1,000 are 39.4 and 19.4 respectiv...
Solution:
Given data:
Annual Birth rate (B) = 39.4 per 1000
Annual Death rate (D) = 19.4 per 1000
We need to calculate the number of years in which the population will be doubled assuming there is no immigration or emigration.
Let the present population be P.
After one year, the population would be P + BP/1000 - DP/1000.
We can write it as:
After one year, the population = P + (B - D)P/1000
= P(1 + r), where r = (B - D)/1000
Now, we need to find the time period in which the population will be doubled.
Let the time period required be T years.
Then, P(1 + r)T = 2P
⇒ (1 + r)T = 2
Taking log on both sides, we get:
T log(1 + r) = log2
T = log2/log(1 + r)
T = log(2)/log(1 + (B - D)/1000)
T = log(2)/log(1 + 20/1000) (Substituting the given values of B and D)
T = log(2)/log(1.02)
T = 35.002
Therefore, the number of years in which the population will be doubled assuming there is no immigration or emigration is 35 years (approximately).
Hence, the correct option is (a) 35 years.
Given data:
Annual Birth rate (B) = 39.4 per 1000
Annual Death rate (D) = 19.4 per 1000
We need to calculate the number of years in which the population will be doubled assuming there is no immigration or emigration.
Let the present population be P.
After one year, the population would be P + BP/1000 - DP/1000.
We can write it as:
After one year, the population = P + (B - D)P/1000
= P(1 + r), where r = (B - D)/1000
Now, we need to find the time period in which the population will be doubled.
Let the time period required be T years.
Then, P(1 + r)T = 2P
⇒ (1 + r)T = 2
Taking log on both sides, we get:
T log(1 + r) = log2
T = log2/log(1 + r)
T = log(2)/log(1 + (B - D)/1000)
T = log(2)/log(1 + 20/1000) (Substituting the given values of B and D)
T = log(2)/log(1.02)
T = 35.002
Therefore, the number of years in which the population will be doubled assuming there is no immigration or emigration is 35 years (approximately).
Hence, the correct option is (a) 35 years.
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The annual birth and death rates per 1,000 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 years. (b) 30 years. (c) 25 years (d) none of these?
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The annual birth and death rates per 1,000 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 years. (b) 30 years. (c) 25 years (d) none of these? 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 annual birth and death rates per 1,000 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 years. (b) 30 years. (c) 25 years (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The annual birth and death rates per 1,000 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 years. (b) 30 years. (c) 25 years (d) none of these?.
The annual birth and death rates per 1,000 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 years. (b) 30 years. (c) 25 years (d) none of these? 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 annual birth and death rates per 1,000 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 years. (b) 30 years. (c) 25 years (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The annual birth and death rates per 1,000 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 years. (b) 30 years. (c) 25 years (d) none of these?.
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