Population Growth

Population Growth

Population Growth

The population of any country does not remain constant. It generally increases. The relative increase of population over an interval of time is called population growth. Growth per unit time is called growth rate.

The way of increasing population is exactly similar to the way of increasing compound amount, because, every year population increases from the previously increased population also.

So, the population of a country or place after T years is given by the formula, 
Population growth formula

    Where, P ----------> Initial population
                        PT ---------> Population after T years
                        R ----------> Rate of growth in % per year
                        T ----------> Time in no. of years

The growth of population is also affected by the number of deaths, in-migrants and out-migrants at the end of the given period of time. In this case,                 
Population growth formula with no. of deaths, in-migrants and out-migrants.

                Where, D ------------> Number of deaths
       Min ----------> In-migrants
                         Mout ---------> Out-migrants

Some other formula,
Some other formula of population growth


Workout Examples

Example 1: The population of a town before 2 years was 75000 and the rate of annual growth of population of the town is 2%. If the number of in-migrants and out-migrants at the end of 2 years were880 and 625 respectively and 550 people died within this time interval, find the present population of the town.

Solution: Here,
                        P = 75000
                        R = 2%
                        Min = 880
                        Mout = 625
                        D = 550
                        PT = ?
            We have, 
Example 1: Solution

                              = 75000 × 1.0404 – 550 + 880 – 625
                              = 78030 – 550 + 880 – 625
                              = 77735

            So, the present population of the town is 77735


Example 2: The present population of a town is 40000. If the yearly birth rate is 5% and death rate is 3%, what will be the population of town after 2 years?

Solution: Here,
                        P = 40000
                        R1 = 5%, R1 = 3%
                        T = 2 years
                        PT = ?
            We have,
Example 2: Solution
                              = 40000 × 1.0404
                              = 41616

            So, the population of the town after 2 years will be 41616.


Example 3: The population of a village increases every year by 5%. At the end of two years, the total population of the village was 10000. If 1025 were migrated to other places, what was the population of the village in the beginning?

Solution: Here,
                        Total population including the migrated number,
PT = 10000 + 1025 = 11025
                        R = 5%
                        T = 2 years
                        Present population, P = ?
            We have,
Example 3: Solution
            or,        11025 = P (1.05)2
            or,        11025 = P × 1.1025
            or,        P = 11025/1.1025
            or,        P = 10000

            So, the population of the village in the beginning was 10000.


Example 4: The population of a town before 3 years was 150000. If the annual growth rates of the population in the last 3 years were 2%, 4% and 5% respectively every year, find the population of the town at the end of 3 years.

Solution: Here,
                        P = 150000
R1 = 2%, R2 = 4% and R3 = 5%
                        T = 3 years
                        PT = ?
            We have,
Example 4: Solution
                              = 150000 × 1.02 × 1.04 × 1.05
                              = 167076

            So, the population of the town at the end of 3 years is 167076.


Example 5: 3years ago, the population of a village was 50000. The population growth rate of village is 2% p.a. 1 year before 420 people died due to an epidemic. Find the present population of the village.

Solution: Here,
                         P = 50000
       R = 2%
       After 2 years (i.e. 1 year before), T = 2 years
Example 5: Solution
       After 2 years, 420 people died due to epidemic. So,
       P = 52020 – 420 = 51600
                        Then, after 1 year (i.e. at present), T = 1 years
Example 5: Solution
            So, the present population of the village is 52632.


You can comment your questions or problems regarding the population growth here.

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