Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2007 Cyprus MO/Lyceum/Problem 2"

m (→‎Solution)
m (→‎See also: +)
Line 8: Line 8:
  
 
==See also==
 
==See also==
−
*[[2007 Cyprus MO/Lyceum/Problems]]
+
{{CYMO box|year=2007|l=Lyceum|num-b=1|num-a=3}}
  
−
*[[2007 Cyprus MO/Lyceum/Problem 1|Previous Problem]]
+
[[Category:Intermediate Algebra Problems]]
−
 
 
−
*[[2007 Cyprus MO/Lyceum/Problem 3|Next Problem]]
 

Revision as of 16:16, 6 May 2007

Problem

Given the formula $f(x) = 4^x$, then $f(x+1)-f(x)$ equals to

$\mathrm{(A) \ } 4\qquad \mathrm{(B) \ } 4^x\qquad \mathrm{(C) \ } 2\cdot4^x\qquad \mathrm{(D) \ } 4^{x+1}\qquad \mathrm{(E) \ } 3\cdot4^x$

Solution

$f(x+1)-f(x)=4^{x+1}-4^x=4\cdot4^x-4^x=(4-1)\cdot4^x=3\cdot4^x\Rightarrow\mathrm{ E}$

See also

2007 Cyprus MO, Lyceum (Problems)
Preceded by
Problem 1 		Followed by
Problem 3
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2007_Cyprus_MO/Lyceum/Problem_2&oldid=14964"