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?

Question

Answer

=}39.4-19.4/1000=0.02,
Now,
2000=1000(1+0.02)^n,
=}2000/1000=1+0.02^n,
=}2=1.02^n,
=}log 2=n log 1.02,
=}n=log 2/log 1.02,
=}n= 0.3010/0.0086,
=}n=35

thank u guys

Answer

Let initial population be 1000
increase in population =1000+39.4-19.4
=1020
%age increase in population is 2%

A =p(1+r/100)^n
2000 =1000(1+2/100)^n

2 = (1.02)^n
n= 17 yrs approx

Answer

Calculation of Population Growth:

To calculate the number of years in which the population will be doubled, we need to consider the birth and death rates. The population growth rate can be determined by subtracting the death rate from the birth rate.

Step 1: Calculate the Population Growth Rate:

Population Growth Rate = Birth Rate - Death Rate

Given:
Birth Rate = 39.4 per 1000
Death Rate = 19.4 per 1000

By substituting the given values into the formula, we can calculate the population growth rate:

Population Growth Rate = 39.4 - 19.4 = 20 per 1000

Step 2: Calculate the Doubling Time:

Next, we need to determine the doubling time, which represents the number of years it takes for a population to double in size. The formula for doubling time is:

Doubling Time = (log(2) / log(1 + Population Growth Rate))

By substituting the population growth rate into the formula:

Doubling Time = (log(2) / log(1 + 0.02))

Calculating this using logarithmic functions, we find that the doubling time is approximately 35 years.

Step 3: Determine the Number of Years:

Finally, to find the number of years in which the population will be doubled, we multiply the doubling time by the number of doublings:

Number of Years = Doubling Time × Number of Doublings

Since we are assuming no immigration or emigration, the number of doublings is equal to 1.

Number of Years = 35 × 1 = 35 years

Therefore, based on the given birth and death rates, the population will be doubled in approximately 35 years.

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