Question

There were 7,20,000 people in a town. If the population of this town increases at the rate of 5% p.a., find the population at the end of 3 years.

Answer 1

We are asked to find the population of a town after 3 years given a 5% annual growth rate. This is a classic compound growth problem.

Step 1: Formula for population growth

`P_("future") = P_("present") (1 + r/100)^n`

Where:

• `P_("future")` = population after n years
• `P_("present")` = 7,20,000
• r = 5%
• n = 3 years

Step 2: Substitute the values

`P_("future") = 7,20,000 (1 + 5/100)^3`

`P_("future") = 7,20,000 (1 + 0.05)^3`

`P_("future") = 7,20,000 xx (1.05)^3`

Step 3: Calculate (1.05)³ step by step

1. 1.05 × 1.05 = 1.1025
2. 1.1025 × 1.05 = 1.157625

Step 4: Multiply by the initial population

`P_("future") = 7,20,000 xx 1.157625`

`P_("future") ≈ 8,33,490`

The population at the end of 3 years is 8,33,490.