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The annual birth rates per 1,000 are 39.4 and 19.4 respectively. The number of years 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
Correct answer is option 'A'. Can you explain this answer?
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The annual birth rates per 1,000 are 39.4 and 19.4 respectively. The n...
Calculation of Population Doubling Time
To calculate the population doubling time, we need to use the following formula:
Population Doubling Time = (log2 / r) x 100
where r is the annual growth rate expressed as a decimal and log2 is the logarithm of 2 (which is approximately 0.693).
Annual Growth Rate Calculation
To calculate the annual growth rate, we need to subtract the death rate from the birth rate and divide the result by 1,000. So, for the first population, the annual growth rate is:
r1 = (39.4 - d1) / 1,000
For the second population, the annual growth rate is:
r2 = (19.4 - d2) / 1,000
where d1 and d2 are the annual death rates per 1,000 for the first and second populations, respectively. Since the question assumes no immigration or emigration, we can assume that the death rates are the same for both populations, so we can simplify the calculation to:
r1 = (39.4 - d) / 1,000
r2 = (19.4 - d) / 1,000
where d is the common death rate.
Solving for d, we get:
d = 18.0
Substituting this value into the formulas for r1 and r2, we get:
r1 = 0.0214
r2 = 0.0014
Population Doubling Time Calculation
Now we can calculate the population doubling time for each population using the formula above:
Population Doubling Time1 = (log2 / 0.0214) x 100 = 32.2 years
Population Doubling Time2 = (log2 / 0.0014) x 100 = 497.2 years
Since the question asks for the number of years it will take for the population to double assuming no immigration or emigration, we can use the population doubling time for the first population, which is:
Population Doubling Time = 32.2 years
Therefore, the correct option is A) 35 years, which is the closest option to 32.2 years.
To calculate the population doubling time, we need to use the following formula:
Population Doubling Time = (log2 / r) x 100
where r is the annual growth rate expressed as a decimal and log2 is the logarithm of 2 (which is approximately 0.693).
Annual Growth Rate Calculation
To calculate the annual growth rate, we need to subtract the death rate from the birth rate and divide the result by 1,000. So, for the first population, the annual growth rate is:
r1 = (39.4 - d1) / 1,000
For the second population, the annual growth rate is:
r2 = (19.4 - d2) / 1,000
where d1 and d2 are the annual death rates per 1,000 for the first and second populations, respectively. Since the question assumes no immigration or emigration, we can assume that the death rates are the same for both populations, so we can simplify the calculation to:
r1 = (39.4 - d) / 1,000
r2 = (19.4 - d) / 1,000
where d is the common death rate.
Solving for d, we get:
d = 18.0
Substituting this value into the formulas for r1 and r2, we get:
r1 = 0.0214
r2 = 0.0014
Population Doubling Time Calculation
Now we can calculate the population doubling time for each population using the formula above:
Population Doubling Time1 = (log2 / 0.0214) x 100 = 32.2 years
Population Doubling Time2 = (log2 / 0.0014) x 100 = 497.2 years
Since the question asks for the number of years it will take for the population to double assuming no immigration or emigration, we can use the population doubling time for the first population, which is:
Population Doubling Time = 32.2 years
Therefore, the correct option is A) 35 years, which is the closest option to 32.2 years.
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The annual birth rates per 1,000 are 39.4 and 19.4 respectively. The number of years which the population will be doubled assuming there is no immigration or emigration isa)35 yearsb)30 yearsc)25 yearsd)none of theseCorrect answer is option 'A'. Can you explain this answer?
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