I came across the following question while going through the Manhattan Math Study Guide.

Q. The no. of people applying to business schools is growing exponentially (not really), such that every 15 years, the number of applicants doubles. As a result, the admission rates are falling, such that every 15 years, the acceptance rate halves. Columbia's is about 8%. When will it be 1%?

I could not form it into an equation, but was able to solve it with the following reasoning:
if no. of students being accepted in this year are 8
then the no. of students who applied=100
after 15 years, the no. of students accepted will be 8
whereas no. who apply will be =200
then in the next 15 years, no. of students who will be accepted will be=8
no. who applied will be=400
and in the 15 years which follow that year, no. accepted =8
whereas no. applied=800
therefore it will be 8/800=1% in the next 45 years

kindly tell me if my method is correct and whether my answer is right; also, if i were to form an equation in terms of F, I, a, n and t then how would it look like?

Thanks!

ok, i just thought about it again; could it be:

1/100=8/100 * 1/2^x?

Both look perfect! Nice job!

_________________
Jamie Nelson
ManhattanGMAT Instructor