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

 
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==Solution==
 
==Solution==
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<math>f(x+1)-f(x)=4^{x+1}-4^x=4\cdot4^x-4^x=4^x\cdot(4-1)=3\cdot4^x\Rightarrow\mathrm{ E}</math>
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<math>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}</math>
  
 
==See also==
 
==See also==

Revision as of 11:28, 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

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