The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:

Given

• Initial population P₀ = 1,75,000
• Population after 10 years P₁₀ = 2,62,500

Concept

The average annual percent increase is the CAGR: ( 𝑃 10 / 𝑃 0 ) 1 / 10 − 1 (P 10 ​ /P 0 ​ ) 1/10 −1.

Step 1: Compute the growth factorGrowth factor = 2 , 62 , 500 1 , 75 , 000 = 1.5 1,75,000 2,62,500 ​ =1.5

Step 2: Compute CAGRCAGR = 1.5 1 / 10 − 1 1.5 1/10 −1Using ln/exponent: ln(1.5) ≈ 0.405465; divide by 10 ⇒ 0.0405465; exp ⇒ 1.04141CAGR ≈ 1.04141 − 1 = 0.04141 = 4.14% per year

Final AnswerAverage percent increase ≈ 4.14% per year.