document.write( "Question 1055333: If Sarah was saving for a computer that cost$1200 the first month she saved$20 and doubled the amount each month after that how many months will it take her to save the money? \n" ); document.write( "
Algebra.Com's Answer #670585 by MathTherapy(10552)\"\" \"About 
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If Sarah was saving for a computer that cost$1200 the first month she saved$20 and doubled the amount each month after that how many months will it take her to save the money?
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Month 1: $20 saved\r\n" );
document.write( "Month 2: 2(20), or $40 saved\r\n" );
document.write( "Month 3: 2(40), or $80 saved\r\n" );
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document.write( "The above represents a GP with the following sequence: \"a%5Bn%5D+=+20%282%29%5E%28n+-+1%29\", with:\r\n" );
document.write( "n = number (month) of the sequence\r\n" );
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document.write( "We now use the sum of a GP, or \"S%5Bn%5D+=+%28a%5B1%5D+-+a%5Bn%5D+%2A+r%29%2F%281+-+r%29\"   \r\n" );
document.write( "\"%221%2C200%22+=+%2820+-+a%5Bn%5D+%2A+2%29%2F%281+-+2%29\" ------- Substituting \r\n" );
document.write( "\"%221%2C200%22+=+%2820+-+2a%5Bn%5D%29%2F%28-+1%29%29\"\r\n" );
document.write( "\"20+-+2a%5Bn%5D+=+-+%221%2C200%22\" -------- Cross-multiplying\r\n" );
document.write( "\"-+2a%5Bn%5D+=+-+%221%2C200%22+-+20\"\r\n" );
document.write( "\"-+2a%5Bn%5D+=+-+%221%2C220%22\"\r\n" );
document.write( "\"a%5Bn%5D+=+%22-+1%2C220%22%2F%28-+2%29\", or $610\r\n" );
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document.write( "As seen above, the term, or month that she will have saved 1,200 or more is the one in which she has saved $610, or more\r\n" );
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document.write( "Now we see that: \"a%5Bn%5D+=+20%282%29%5E%28n+-+1%29\" becomes:\r\n" );
document.write( "\"610+=+20%282%29%5E%28n+-+1%29\"\r\n" );
document.write( "\"610%2F20+=+2%5E%28n+-+1%29\" ------ Dividing by 20\r\n" );
document.write( "\"61%2F2+=+2%5E%28n+-+1%29\"\r\n" );
document.write( "\"log+%282%2C+%2861%2F2%29%29+=+n+-+1\" ------- Converting to LOGARITHMIC form\r\n" );
document.write( "n, or month in which she will have saved $610 = \"log+%282%2C+%2861%2F2%29%29+%2B+1\", or \"highlight_green%28matrix%281%2C6%2C+5.930737%2C+or%2C+close%2C+to%2C+month%2C+6%29%29\". \r\n" );
document.write( "This means that in month 5, she would NOT HAVE realized her goal of $1,200, but in month 6, she would’ve saved more than the $1,200 (see table below).\r\n" );
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document.write( "OR\r\n" );
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document.write( "The EASIEST METHOD:\r\n" );
document.write( "Month     Amount Saved     Total Saved\r\n" );
document.write( "  1           $20              $20\r\n" );
document.write( "  2      2(20)  =  $40         $60\r\n" );
document.write( "  3      2(40)  =  $80        $140\r\n" );
document.write( "  4      2(80)  = $160        $300\r\n" );
document.write( "  5      2(160) = $320        $620\r\n" );
document.write( "  6      2(320) = $640      $1,260
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