document.write( "Question 1155415: Hello, can someone please help me with this problem:
\n" ); document.write( "Use the properties of exponents to rewrite y=4e^{-0.5t} in the form y=a(1+r)^t or y=a(1-r)^t . Round the value of r to the nearest thousandth. Then find the percent rate of change to the nearest tenth of percent.
\n" ); document.write( "I really need to know what the percent rate of change is.
\n" ); document.write( "I have tried but I really just don't understand how to do it.
\n" ); document.write( "Please help, Thanks. \n" ); document.write( "
Algebra.Com's Answer #778000 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Her answer is correct, but she used logarithms.  Maybe you aren't supposed to\r\n" );
document.write( "use logarithms. Maybe you're not studying logarithms yet.  Anyway, here's\r\n" );
document.write( "how without using logarithms. \r\n" );
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document.write( "Rewrite y=4e^{-0.5t} in the form y=a(1+r)^t \r\n" );
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document.write( "   \"4e%5E%28-0.5t%29+=+a%281%2Br%29%5Et\"\r\n" );
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document.write( "If those are to be identical, then regardless of what number we choose\r\n" );
document.write( "to substitute for t, both sides of that equation must be equal.\r\n" );
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document.write( "The easiest number to substitute is 0.\r\n" );
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document.write( "   \"4e%5E%28-0.5%280%29%29+=+a%281%2Br%29%5E%280%29\"\r\n" );
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document.write( "   \"4e%5E0+=+a%281%2Br%29%5E0\"\r\n" );
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document.write( "Since anything raised to the zero power is 1 [With one exception, the undefined\r\n" );
document.write( "00, which is of no concern to us here.]\r\n" );
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document.write( "So the above equation becomes:\r\n" );
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document.write( "   \"4%281%29+=+a%281%29\"\r\n" );
document.write( "     \"4=a\"\r\n" );
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document.write( "So \"a\" is 4.  So we substitute 4 for a:\r\n" );
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document.write( "   \"4e%5E%28-0.5t%29+=+4%281%2Br%29%5Et\"\r\n" );
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document.write( "We divide both sides by 4\r\n" );
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document.write( "   \"e%5E%28-0.5t%29+=+%281%2Br%29%5Et\"\r\n" );
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document.write( "Now we substitute t=1\r\n" );
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document.write( "   \"e%5E%28-0.5%2A1%29+=+%281%2Br%29%5E1\"\r\n" );
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document.write( "   \"e%5E%28-0.5%29+=+%281%2Br%29%5E1\"\r\n" );
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document.write( "   \"e%5E%28-0.5%29+=+1%2Br\"\r\n" );
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document.write( "   \"e%5E%28-0.5%29-1+=+r\"\r\n" );
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document.write( "You can rewrite r as\r\n" );
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document.write( "\"e%5E%28-0.5%29+=+e%5E%28-1%2F2%29+=+1%5E%22%22%2Fe%5E%281%2F2%29+=+1%2Fsqrt%28e%29\"\r\n" );
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document.write( "which she did.\r\n" );
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document.write( "So to write \r\n" );
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document.write( "y=4e^{-0.5t} in the form y=a(1+r)^t is to write it\r\n" );
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document.write( "\"y=4%281%2B%281%2Fsqrt%28e%29-1%29%5E%22%22%29%5Et\"\r\n" );
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document.write( "And that simplifies to her answer, which is correct but not quite in\r\n" );
document.write( "the form you asked for.  \r\n" );
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document.write( "Edwin
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