1981 AHSME Problems/Problem 13
Problem
Suppose that at the end of any year, a unit of money has lost of the value it had at the beginning of that year. Find the smallest integer such that after years, the money will have lost at least of its value (To the nearest thousandth ).
Solution
What we are trying to solve is . This turns into We know that , thus by log rules we have , thus , and our answer is .
-edited by Maxxie and maxamc