Difference between revisions of "2001 AIME II Problems/Problem 8"
(solution) |
|||
Line 20: | Line 20: | ||
[[Category:Intermediate Algebra Problems]] | [[Category:Intermediate Algebra Problems]] | ||
+ | {{MAA Notice}} |
Revision as of 19:35, 4 July 2013
Problem
A certain function has the properties that for all positive real values of , and that for . Find the smallest for which .
Solution
Iterating the condition , we find that for positive integers . We know the definition of from , so we would like to express . Indeed,
We now need the smallest such that . The range of , is . Then , and the smallest value of is . Then,
We want the smaller value of .
An alternative approach is to consider the graph of , which repeats every power of , and resembles the section from expanded by a factor of .
See also
2001 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.