document.write( "Question 1072878: 4. The value of a lathe originally valued at £3000 depreciates 15% per annum. Calculate its value after 4 years. The machine is sold when its value is less than £550. After how many years is the lathe sold? \n" ); document.write( "
Algebra.Com's Answer #687733 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "When something depreciates and 15%, its value\r\n" );
document.write( "is multiplied by 100%-15% or 85% or 0.85.\r\n" );
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document.write( "So the geometric sequence is \r\n" );
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document.write( "After     \r\n" );
document.write( " this      The\r\n" );
document.write( "Number    value    \r\n" );
document.write( "  of       of\r\n" );
document.write( "years     the     \r\n" );
document.write( "have      lathe\r\n" );
document.write( "passed     is \r\n" );
document.write( "----------------------\r\n" );
document.write( "  0       £3000\r\n" );
document.write( "  1       £2550 \r\n" );
document.write( "  2       £2167.50\r\n" );
document.write( "  3       £1842.375\r\n" );
document.write( "  4       £1566.01875\r\n" );
document.write( "  5       £1551.115938\r\n" );
document.write( "  6       £1121.448547\r\n" );
document.write( "  7       £ 961.7312648\r\n" );
document.write( "  8       £ 817.4715751\r\n" );
document.write( "  9       £ 694.8508388\r\n" );
document.write( " 10       £ 590.623213\r\n" );
document.write( " 11       £ 502.0297311\r\n" );
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document.write( "The lathe will be sold after 11 years.\r\n" );
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document.write( "That's the easiest way, but your teacher perhaps\r\n" );
document.write( "wants you do it using the formula for the nth term\r\n" );
document.write( "of a geometric series:\r\n" );
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document.write( "By formula, a1 = £3000, r = 0.85\r\n" );
document.write( "\r\n" );
document.write( "\"a%5B1%5D%2Ar%5E%28n-1%29\"\"%22%22%3C%22%22\"\"550\"\r\n" );
document.write( "\"3000%2A%280.85%29%5E%28n-1%29\"\"%22%22%3C%22%22\"\"550\"\r\n" );
document.write( "\"%280.85%29%5E%28n-1%29\"\"%22%22%3C%22%22\"\"550%2F3000\"\r\n" );
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document.write( "Take logarithms of both sides (you may use\r\n" );
document.write( "either base logarithms, natural or common))\r\n" );
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document.write( "\"log%28%280.85%29%5E%28n-1%29%29%29\"\"%22%22%3C%22%22\"\"log%28%28550%2F3000%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28n-1%29log%28%280.85%29%29\"\"%22%22%3C%22%22\"\"log%28%2811%2F60%29%29\"\r\n" );
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document.write( "Since log(0.85) is negative, we must reverse\r\n" );
document.write( "the inequality symbol from < to > when we\r\n" );
document.write( "divide both sides by log(0.85)\r\n" );
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document.write( "\"n-1\"\"%22%22%3E%22%22\"\"log%28%2811%2F60%29%29%2Flog%28%280.85%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"n-1\"\"%22%22%3E%22%22\"\"10.5401789\"\r\n" );
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document.write( "\"n\"\"%22%22%3E%22%22\"\"11.5401789\"\r\n" );
document.write( " \r\n" );
document.write( "The lathe will be sold after 11 years.\r\n" );
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document.write( "Edwin
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