Question

The present population of a town is 48400. It is increasing 10% every year. Find the population of the town:

1. 2 years ago, 
2. After 2 years.

Answer 1

Given:

• Present population of the town (P₀ = 48400)
• Annual increase rate (r = 10%)

i. Population 2 years ago

Step 1: Let the population 2 years ago be P.

Step 2: Population grows by 10% each year, hence the present population after 2 years can be expressed as:

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

P₀ = P × (1.1)²

P₀ = P × 1.21

Step 3: Solve for P:

`P = P_0/1.21`

`P = 48400/1.21`

P = 40000

ii. Population after 2 years

Step 1: Let the population after 2 years be P₂.

Step 2: Population increases by 10% each year, so:

`P_2 = P_0 xx (1 + r/100)^2`

P₂ = 48400 × (1.1)²

P₂ = 48400 × 1.21

P₂ = 58564