Question

The population of a village increases 10% every year. If its present population is 12,100, find its population:

1. 2 years ago,
2. After 2 years.

Answer 1

Given:

• Present population (P₀ = 12,100)
• Population increases by 10% every year, i.e. rate (r = 10%)

We need to find:

1. Population 2 years ago (P) 
2. Population after 2 years (P_after)

Step-wise calculation:

i. Population 2 years ago

The population grows according to the formula:

`P_0 = P xx (1 + r/100)^2`

Rearranged to find (P) population 2 years ago:

`P = P_0/(1 + r/100)^2`

`P = 12100/(1.10)^2`

`P = 12100/1.21`

P = 10,000

ii. Population after 2 years

Using the formula for future population growth:

`P_"after" = P_0 xx (1 + r/100)^2`

P_after = 12100 × (1.10)²

P_after = 12100 × 1.21

P_after = 14,641

Population 2 years ago = 10,000.

Population after 2 years = 14,641.