document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189652>Question 1189652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, any chance I could get some help with this question?\r<BR>\n" );
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document.write( "Thanks in advance!\r<BR>\n" );
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document.write( "https://drive.google.com/file/d/1aP4pFGQqFN3nVsqZb0HjqpvFIz26JHwd/view?usp=sharing </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821077 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=821077\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> table of values is:\r<BR>\n" );
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document.write( "time(days)           remaining amount of sucralose(mg)\r\n" );
document.write( "0                             40\r\n" );
document.write( "2                             20\r\n" );
document.write( "4                             10\r\n" );
document.write( "6                             5\r\n" );
document.write( "8                             2.5\r\n" );
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document.write( "formula is y = a * b^x<BR>\n" );
document.write( "a is the initial value.<BR>\n" );
document.write( "b is the base for the exponent.<BR>\n" );
document.write( "x is the exponent.\r<BR>\n" );
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document.write( "from the table, you get 40 = 40 * b^0.<BR>\n" );
document.write( "since b^0 is always equal to 1, you get 40 = 40 and b is still undefined.\r<BR>\n" );
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document.write( "from the table, you get 20 = 40 * b^2.<BR>\n" );
document.write( "solve for b^2 to get:<BR>\n" );
document.write( "b^2 = .5<BR>\n" );
document.write( "solve for b to get:<BR>\n" );
document.write( "b = .7071067812.\r<BR>\n" );
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document.write( "from the table, you get 10 = 40 * b^4.<BR>\n" );
document.write( "solve for b^4 to get:<BR>\n" );
document.write( "b^4 = .25<BR>\n" );
document.write( "solve for b to get:<BR>\n" );
document.write( "b = .25^(1/4) = .7071067812.\r<BR>\n" );
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document.write( "from the table, you get 5 = 40 * b^6.<BR>\n" );
document.write( "solve for b^6 to get:<BR>\n" );
document.write( "b^6 = 1/8<BR>\n" );
document.write( "solve for b to get:<BR>\n" );
document.write( "b = (1/8)^(1/6) = .7071067812.\r<BR>\n" );
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document.write( "this very much indicates that b = .7071067812.\r<BR>\n" );
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document.write( "your formula is y = 40 * (.7071067812) ^ x\r<BR>\n" );
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document.write( "note that sqrt(.5) = .7071067812.\r<BR>\n" );
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document.write( "you can graph this formula.<BR>\n" );
document.write( "it looks like this:\r<BR>\n" );
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document.write( "your unrounded formula is:\r<BR>\n" );
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document.write( "y = 40 * .7071067812 ^ x\r<BR>\n" );
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document.write( "your rounded formula is:\r<BR>\n" );
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document.write( "y = 40 * .71 ^ x\r<BR>\n" );
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document.write( "your rate of decay is 50% every 2 days.\r<BR>\n" );
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document.write( "every day, the amount of sucralose in the body is .7071067812 times the amount in the previous day.\r<BR>\n" );
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document.write( "that's a loss of (1 - .7071067812) = .2928932188 * the amount of sucralose from the previous day.\r<BR>\n" );
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document.write( "on day 0 you have 40.<BR>\n" );
document.write( "on day 1 you have .7071067812 * 40 = 28.28427125.<BR>\n" );
document.write( "that's a loss of 40 - 28.28427125 = 11.71572875 sucralos.<BR>\n" );
document.write( "that is 11.71572875 / 40 = a loss of .2928932188 = 29.28932188%.\r<BR>\n" );
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document.write( "the rounded rate of decay formula is:<BR>\n" );
document.write( "y = 40 * .71 ^ x<BR>\n" );
document.write( "every day, you have .71 * the amount of sucralose in your body that you had the previous day.\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo<BR>\n" );
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