document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155461>Question 1155461</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, can someone please help me with this problem:<BR>\n" );
document.write( "Rewrite  y=5(1/4)^{t/6} in the form y=a(1+r)^t or y=a(1-r)^t. Round the value of r to the nearest ten-thousandth. Then tell whether the model represents exponential growth or exponential decay.\r<BR>\n" );
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document.write( "I know that it represents exponential decay but I don't understand how to rewrite in that form.\r<BR>\n" );
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document.write( "Someone, please help. Thanks   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #778047 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=778047\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%281%2F4%29%5E%28t%2F6%29 ALIGN=MIDDLE  ALT=\"y=5%281%2F4%29%5E%28t%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%281%2Br%29%5Et ALIGN=MIDDLE  ALT=\"y=a%281%2Br%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%281-r%29%5Et ALIGN=MIDDLE  ALT=\"y=a%281-r%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%281%2F4%29%5E%28t%2F6%29=5%281%2Br%29%5Et ALIGN=MIDDLE  ALT=\"5%281%2F4%29%5E%28t%2F6%29=5%281%2Br%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > .....simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%5E%28t%2F6%29=%281%2Br%29%5Et+ ALIGN=MIDDLE  ALT=\"%281%2F4%29%5E%28t%2F6%29=%281%2Br%29%5Et+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%5E2%29%5E%28t%2F6%29=%281%2Br%29%5Et+ ALIGN=MIDDLE  ALT=\"%281%2F2%5E2%29%5E%28t%2F6%29=%281%2Br%29%5Et+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E-2%29%5E%28t%2F6%29=%281%2Br%29%5Et+ ALIGN=MIDDLE  ALT=\"%282%5E-2%29%5E%28t%2F6%29=%281%2Br%29%5Et+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C+%22%22%2C2%5E%28-2t%2F6%29=%281%2Br%29%5Et%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C+%22%22%2C2%5E%28-2t%2F6%29=%281%2Br%29%5Et%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C+%22%22%2C2%5E%28-t%2F3%29=%281%2Br%29%5Et%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C+%22%22%2C2%5E%28-t%2F3%29=%281%2Br%29%5Et%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....take log of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%5E%28-t%2F3%29%29=log%28%281%2Br%29%5Et+%29 ALIGN=MIDDLE  ALT=\"log%282%5E%28-t%2F3%29%29=log%28%281%2Br%29%5Et+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-t%2F3%29log%282%29=t%2Alog%28%281%2Br%29+%29 ALIGN=MIDDLE  ALT=\"%28-t%2F3%29log%282%29=t%2Alog%28%281%2Br%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-t%2F3%29log%282%29%2Ft=log%28%281%2Br%29+%29 ALIGN=MIDDLE  ALT=\"%28-t%2F3%29log%282%29%2Ft=log%28%281%2Br%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F3%29log%282%29=log%28%281%2Br%29+%29 ALIGN=MIDDLE  ALT=\"-%281%2F3%29log%282%29=log%28%281%2Br%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%5E%28-1%2F3%29%29=log%28%281%2Br%29%29 ALIGN=MIDDLE  ALT=\"log%282%5E%28-1%2F3%29%29=log%28%281%2Br%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C+%22%22%2Clog%281%2F2%5E%281%2F3%29%29%29=log%28%281%2Br%29+%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C+%22%22%2Clog%281%2F2%5E%281%2F3%29%29%29=log%28%281%2Br%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...if log  same, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Froot%283%2C2%29=1%2Br ALIGN=MIDDLE  ALT=\"1%2Froot%283%2C2%29=1%2Br\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=+1%2Froot%283%2C2%29+-+1 ALIGN=MIDDLE  ALT=\"r=+1%2Froot%283%2C2%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%281%2Br%29%5Et ALIGN=MIDDLE  ALT=\"y=a%281%2Br%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%281%2B1%2Froot%283%2C2%29+-+1%29%5Et ALIGN=MIDDLE  ALT=\"y=5%281%2B1%2Froot%283%2C2%29+-+1%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%281%2Froot%283%2C2%29+%29%5Et ALIGN=MIDDLE  ALT=\"y=5%281%2Froot%283%2C2%29+%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check if:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%281%2F4%29%5E%28t%2F6%29=5%281%2Froot%283%2C2%29+%29%5Et+ ALIGN=MIDDLE  ALT=\"5%281%2F4%29%5E%28t%2F6%29=5%281%2Froot%283%2C2%29+%29%5Et+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> true\r<BR>\n" );
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document.write( "in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%281-r%29%5Et ALIGN=MIDDLE  ALT=\"y=a%281-r%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%281-%281%2Froot%283%2C2%29+-+1%29%29%5Et ALIGN=MIDDLE  ALT=\"y=5%281-%281%2Froot%283%2C2%29+-+1%29%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%281-1%2Froot%283%2C2%29+%2B+1%29%5Et ALIGN=MIDDLE  ALT=\"y=5%281-1%2Froot%283%2C2%29+%2B+1%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%282-1%2Froot%283%2C2%29+%29%5Et ALIGN=MIDDLE  ALT=\"y=5%282-1%2Froot%283%2C2%29+%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%281%2F4%29%5E%28t%2F6%29%3C%3E5%282-1%2Froot%283%2C2%29+%29%5Et ALIGN=MIDDLE  ALT=\"5%281%2F4%29%5E%28t%2F6%29%3C%3E5%282-1%2Froot%283%2C2%29+%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> not true\r<BR>\n" );
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document.write( "so, your answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%281%2Froot%283%2C2%29+%29%5Et ALIGN=MIDDLE  ALT=\"y=5%281%2Froot%283%2C2%29+%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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