document.write( "Question 1076999: The number of frogs in a lake decrease by x% each year.
\n" ); document.write( "Given that the number of frogs halves in 8 years, work out the value of x.
\n" ); document.write( "Give your answer correct to 1 decimal place. \n" ); document.write( "

Algebra.Com's Answer #691559 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
As a decimal, x% = $\"+.01x+\"$
\n" ); document.write( "Let $\"+N+\"$ = the number of frog to begin with
\n" ); document.write( " $\"+N%2F2+\"$ = the number of frogs after $\"+8+\"$ yrs
\n" ); document.write( "------------------------------------------
\n" ); document.write( " $\"+N%2F2+=+N%2A%28+1+-+.01x+%29%5E8+\"$
\n" ); document.write( "Divide both sides by $\"+N+\"$
\n" ); document.write( " $\"+1%2F2+=+%28+1+-+.01x+%29%5E8+\"$
\n" ); document.write( "Take the eigthth root of both sides
\n" ); document.write( " $\"+%28+1%2F2+%29%5E%281%2F8%29+=+1+-+.01x+\"$
\n" ); document.write( " $\"+.917+=+1+-+.01x+\"$
\n" ); document.write( " $\"+.01x+=+1+-+.917+\"$
\n" ); document.write( " $\"+.01x+=+.083+\"$
\n" ); document.write( " $\"+x+=+8.3+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2F2+=+%28+1+-+.01x+%29%5E8+\"$
\n" ); document.write( " $\"+1%2F2+=+%28+1+-+.083+%29%5E8+\"$
\n" ); document.write( " $\"+.5+=+.917%5E8+\"$
\n" ); document.write( " $\"+.5+=+.49998+\"$
\n" ); document.write( "close enough
\n" ); document.write( "check the math\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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