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2007 Cyprus MO/Lyceum/Problem 2

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Problem

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

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

Solution

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

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 "http://www.artofproblemsolving.com/Wiki/index.php/2007_Cyprus_MO/Lyceum/Problem_2"

Category: Introductory Algebra Problems

Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.

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