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

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

R₁ = 5%, R₁ = 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

R₁ = 2%, R₂ = 4% and R₃ = 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