Question

As a town gets smaller, the population of its high school decreases by 6% each year, teh senior class has 250 students now. in how many years will it have about 100 students

Answer 1

An equation to solve for the time when the high school will have exactly 100 students is (1-.06)^x = (250/100).
That simplifies to 94^x = .4.
We can then take the log of both sides to isolate the x variable from the exponent. Here's with natural log.
x*ln(.94)=ln(.4)
x = ln(.4)/ln(.94)
Solving this gives x ~= 14.80. So in about 15 years, the high school will have 100 students.