document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=156723>Question 156723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem on Non-linear Functions.- The amount of medicine left in a person's body after ingesting it is represented in the table below:\r<BR>\n" );
document.write( "\n" );
document.write( "Hours  / Amount of Medicine (mg)<BR>\n" );
document.write( "  0    /         100(mg)<BR>\n" );
document.write( "  1    /         50(mg)<BR>\n" );
document.write( "  2    /         25(mg)<BR>\n" );
document.write( "  3    /         12.5(mg)<BR>\n" );
document.write( "  4    /         3.125(mg)<BR>\n" );
document.write( "  5    /         1.5625(mg)  1.How do you calculate the amount of medicine left in the body according to the pattern in table? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #115571 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=115571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you look at the given data as ordered pairs (x, y), you can plot these on a graph and begin to see some kind of relationship between the elapsed hours (the indepedent variable, x) and the amount of medicine remaining (the dependent variable, y).<BR>\n" );
document.write( "You'll notice that for each hour that elapses, the amount of medicine remaining is half the previous amount.  This suggests a decaying exponential function that might look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100%2F2%5Ex ALIGN=MIDDLE  ALT=\"y+=+100%2F2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's try a few values of the independent variable (hours elapsed, x) and see if we get the corresponding amount of medicine left as shown by the table of data.<BR>\n" );
document.write( "Starting with x = 0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100%2F2%5E0 ALIGN=MIDDLE  ALT=\"y+=+100%2F2%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100%2F1 ALIGN=MIDDLE  ALT=\"y+=+100%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100 ALIGN=MIDDLE  ALT=\"y+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Good!<BR>\n" );
document.write( "x = 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100%2F2%5E1 ALIGN=MIDDLE  ALT=\"y+=+100%2F2%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100%2F2 ALIGN=MIDDLE  ALT=\"y+=+100%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+50 ALIGN=MIDDLE  ALT=\"y+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" > Good!<BR>\n" );
document.write( "x = 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100%2F2%5E2 ALIGN=MIDDLE  ALT=\"y+=+100%2F2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100%2F4 ALIGN=MIDDLE  ALT=\"y+=+100%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+25 ALIGN=MIDDLE  ALT=\"y+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Good!<BR>\n" );
document.write( "x = 3:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100%2F2%5E3 ALIGN=MIDDLE  ALT=\"y+=+100%2F2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100%2F8 ALIGN=MIDDLE  ALT=\"y+=+100%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+12.5 ALIGN=MIDDLE  ALT=\"y+=+12.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Good!<BR>\n" );
document.write( "x = 4:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100%2F2%5E4 ALIGN=MIDDLE  ALT=\"y+=+100%2F2%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100%2F16 ALIGN=MIDDLE  ALT=\"y+=+100%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+6.25 ALIGN=MIDDLE  ALT=\"y+=+6.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now this does not follow the previous pattern, so I would question whether or not the table has all of the data.<BR>\n" );
document.write( "x = 5:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100%2F2%5E5 ALIGN=MIDDLE  ALT=\"y+=+100%2F2%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+100%2F32 ALIGN=MIDDLE  ALT=\"y+=+100%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3.125 ALIGN=MIDDLE  ALT=\"y+=+3.125\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the result shown for x (elapsed hours) = 4 .<BR>\n" );
document.write( "Could you perhaps have copied the data wrongly?<BR>\n" );
document.write( "Let's look at the curve:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C10%2C-5%2C100%2C100%2F2%5Ex%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C10%2C-5%2C100%2C100%2F2%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take a look at your original data to see if you have skipped an entry. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );