##
**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,

Where, P ----------> Initial population

P

_{T}---------> 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,

_{ }Where, D ------------> Number of deaths

M

_{in}----------> In-migrants
M

_{out}---------> Out-migrants
Some other formula,

###
*Workout
Examples*

*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%*

*M*_{in}= 880

*M*_{out}= 625

*D = 550*

*P*_{T}= ?

*We have,*

*= 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*

*R*_{1}= 5%, R_{1}= 3%

*T = 2 years*

*P*_{T}= ?

*We have,*

*= 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,*

*P*_{T}= 10000 + 1025 = 11025

*R = 5%*

*T = 2 years*

*Present population, P = ?*

*We have,*

*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*

*R*_{1}= 2%, R_{2}= 4% and R_{3}= 5%

*T = 3 years*

*P*_{T}= ?

*We have,*

*= 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*

*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*

*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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