The initial population of a town was 12,500 and was projected to grow at a rate of 2.5% per decade. Write an expression for the projected population of Round Rock after n decades.

Question

 The initial population of a town was 12,500 and was projected to grow at a rate of 2.5% per decade. Write an expression for the projected population of Round Rock after n decades. 

Answer 1

After one decade the new population will be 12500 * 102.5/100

After two decade the new population will grow 2.5% again from the previous decade (12500 * 102.5/100)

So the population after two decades (n = 2) will be

(12500 * 102.5/100) * 102.5/100

Or it can be said

12500 * (102.5/100)^2

After three decade the new population will grow 2.5% again from the previous decade (12500 * 102.5/100 *102.5/100)

So the population after two decades (n = 3) will be

(12500 * 102.5/100 * 102.5/100) * 102.5/100

Or it can be said

12500 * (102.5/100)^3

Expressiom for projected population after n decades will be

12500 * (102.5/100)^n

Or

12500 * (1.025)^n