jmc

Question

The capacity of a school is 1100 students and the current enrollment is 980 students. If the student population increases at a rate of 5 percent per year, what is the smallest integer n such that the enrollment will exceed the capacity in n years?

Accepted Answer

Five percent of 980 is 980/20=49, so after one year the enrollment will be 980+49=1029. Five percent of 1029 is 49+5%(49)=51920, so at the end of the second year, there will be 1029+51910=1080920 students (or, rather, 1080 students). Five percent of 1080920 is greater than 50, so at the end of 3 years, there will be more than 1100 students.