document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890503>Question 890503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A particular substances decays in such a way that it loses half its weight each day. In how many days will 256 g of the substances to reduced to 32 g? How much of the substance is left after 10 days? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539029 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=539029\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for growth is:\r<BR>\n" );
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document.write( "f = p * (1 + r)^n\r<BR>\n" );
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document.write( "r is the growth rate per time period.<BR>\n" );
document.write( "n is the number of time periods.<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "f is the future value.\r<BR>\n" );
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document.write( "in your problem:\r<BR>\n" );
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document.write( "f = 32<BR>\n" );
document.write( "p = 256 <BR>\n" );
document.write( "r = -.5<BR>\n" );
document.write( "1+r = .5<BR>\n" );
document.write( "n is what you have to solve for.\r<BR>\n" );
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document.write( "the equation becomes:\r<BR>\n" );
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document.write( "32 = 298 * (.5)^n\r<BR>\n" );
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document.write( "divide both sides of this equation by 298 to get:\r<BR>\n" );
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document.write( "32/298 = .5^n\r<BR>\n" );
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document.write( "take the log of both sides of this equation to get:\r<BR>\n" );
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document.write( "log(32/298) = log(.5^n)\r<BR>\n" );
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document.write( "since log(.5^n) = n * log(.5), your equation becomes:\r<BR>\n" );
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document.write( "log(32/298) = n * log(.5)\r<BR>\n" );
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document.write( "divide both sides of this equation by log(.5) to get:\r<BR>\n" );
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document.write( "log(32/298) / log(.5) =  n\r<BR>\n" );
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document.write( "use your calculator to solve for n to get:\r<BR>\n" );
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document.write( "n = 3.21916852...\r<BR>\n" );
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document.write( "store that in your calculator and use it to confirm the solution is correct.\r<BR>\n" );
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document.write( "your original equation becomes:\r<BR>\n" );
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document.write( "32 = 298 * (.5)^3.21916852...\r<BR>\n" );
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document.write( "you get 32 = 32\r<BR>\n" );
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document.write( "this confirms your calculations are correct.\r<BR>\n" );
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document.write( "256 grams of the substance will be reduced to 32 grams in 3.21916852... days if it loses half its weight each day.\r<BR>\n" );
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document.write( "start with 298.<BR>\n" );
document.write( "at end of 1 day, you have 149<BR>\n" );
document.write( "at end of 2 days, you have 74.5<BR>\n" );
document.write( "at end of 3 days, you have 37.25<BR>\n" );
document.write( "at end of 3.21916852... days, you have 32.\r<BR>\n" );
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document.write( "that fractional part of the last day is calculated as follows:\r<BR>\n" );
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document.write( "37.25 * .5^.21916852... = 32\r<BR>\n" );
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document.write( "after 10 days, you will be left with 298 * .5^10 = .291015625 grams.\r<BR>\n" );
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document.write( "you can see the day by day effect by looking at the following table:\r<BR>\n" );
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document.write( "         day        grams\r\n" );
document.write( "          0          298\r\n" );
document.write( "          1          149\r\n" );
document.write( "          2          74.5\r\n" );
document.write( "          3          37.25\r\n" );
document.write( "          3.2191...  32\r\n" );
document.write( "          4          18.625\r\n" );
document.write( "          5          9.3125\r\n" );
document.write( "          6          4.6563\r\n" );
document.write( "          7          2.23281\r\n" );
document.write( "          8          1.1641\r\n" );
document.write( "          9          .58203\r\n" );
document.write( "          10         .29102\r\n" );
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document.write( " </SPAN>\n" );
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