Each year a population grows by the factor 1+1.6% = 1+1.6/100 = 1.016 (denote this as a). I.e. to obtain a population after one year we have to multiply the initial value 100,000 (denote it as b) by a. One year later — multiply (b*a) by a, obtaining b*a^2. Then b*a^3 and so on.
After full ten years the value will be b*a^10 = 100,000*(1.016)^10 = approx. 117,203 people.