Population in the zeroth year = 25000
After 1 year it increases to 3%, that is 100% + 3% = 103% = 103/100 = 1.03
So it increases by a multiplying factor of 1.03.
At the end of year 1 = 25000*1.03
At the end of year 2 = 25000*1.03*1.03 = 25000*1.03²
At the end of year 3 = 25000*1.03*1.03*1.03 = 25000*1.03³
...
....
Similarly at the end of 10 years = 25000*1.03¹⁰ evaluate with calculator.
= 25000*1.03¹⁰ ≈ 33 597.91
So the population at the end of 10 years will be ≈ 33 598
Hope this explains it.
