document.write( "Question 190889This question is from textbook saxon algebra 2
\n" ); document.write( ": If $500 is invested at 7% compounded continuously, how long would it take for the value of the investment to reach $800? \n" ); document.write( "
Algebra.Com's Answer #143374 by Edwin McCravy(20060)\"\" \"About 
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If $500 is invested at 7% compounded continuously, how long would it take for the value of the investment to reach $800?
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document.write( "The equation for continuous compounding is\r\n" );
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document.write( "\"A+=+Pe%5E%28rt%29\"\r\n" );
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document.write( "where \r\n" );
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document.write( "P = the Principal, which is the same as the starting amount = $500\r\n" );
document.write( "A = the AFTER amount, which is the same as the ending amount = $800\r\n" );
document.write( "r = the rate expressed as a decimal, 0.07\r\n" );
document.write( "t = the number of years it takes for the Principal to become the \r\n" );
document.write( "    AFTER amount.  That's the unknown that we want to find.\r\n" );
document.write( "e = 2.718281828459\r\n" );
document.write( "So we substitute everything but t in\r\n" );
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document.write( "\"A+=+Pe%5E%28rt%29\"\r\n" );
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document.write( "\"800+=+500e%5E%28.07t%29\"\r\n" );
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document.write( "Divide both sides by 500\r\n" );
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document.write( "\"1.6+=+e%5E%28.07t%29\"\r\n" );
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document.write( "Use this rule: \r\n" );
document.write( "The exponential equation\"A+=+e%5EB\" is equivalent to \"B=ln%28A%29\"\r\n" );
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document.write( "\".07t=ln%281.6%29\"\r\n" );
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document.write( "Divide both sides by .07:\r\n" );
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document.write( "\"t+=+ln%281.6%29%2F.07\"\r\n" );
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document.write( "\"t+=+6.714337561\"\r\n" );
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document.write( "About 6.7 years.\r\n" );
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document.write( "Edwin
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