Question

A town has a population of 32,000 in the year 2002; 38,400 in the year 2003; 46,080 in the year 2004; and 55,296 in the year 2005. if this pattern continues, what will the population be in the year 2015?

Answer 1

The point is to find the growth rate. The compound formula is:

P=A(1+ growth rate)ⁿ, where A is the initial Value & P the new value after n years:
P₂₀₀₃ =P₂₀₀₂ (1+ growth rate)¹ (the period "n" from 2002 to 2003 being 1 year)

38400 = 32000(1+growth rate)¹
38400 / 32000 - 1= growth rate & growth rate = 1/5 = 0.2
You will balso find the same growth rate for:
P₂₀₀₄ = P₂₀₀₃(1+ growth rate)¹
P₂₀₀₅ = P₂₀₀₄((1+ growth rate)¹
between 2015 & 2002 THERE ARE 14 YEARS:

P₂₀₁₅ = P₂₀₀₂(1+0.2)¹⁴ & P₂₀₁₅ = 32000(1+02)¹⁴ = 410,854