document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155415>Question 1155415</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, can someone please help me with this problem:<BR>\n" );
document.write( "Use the properties of exponents to rewrite y=4e^{-0.5t} in the form y=a(1+r)^t or y=a(1-r)^t . Round the value of r to the nearest thousandth. Then find the percent rate of change to the nearest tenth of percent. <BR>\n" );
document.write( "I really need to know what the percent rate of change is.<BR>\n" );
document.write( "I have tried but I really just don't understand how to do it.<BR>\n" );
document.write( "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 #777993 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=777993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4e%5E%28-0.5t%29+ ALIGN=MIDDLE  ALT=\"y=4e%5E%28-0.5t%29+\"   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;\" > 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( "first you need to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > that makes following statement true\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-0.5t%29+=%281%2Br%29%5Et ALIGN=MIDDLE  ALT=\"e%5E%28-0.5t%29+=%281%2Br%29%5Et\"   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%28e%5E%28-0.5t%29+%29=log%28%281%2Br%29%5Et%29 ALIGN=MIDDLE  ALT=\"log%28e%5E%28-0.5t%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=%28-0.5t%29log%28e+%29=t%2Alog%28%281%2Br%29%29 ALIGN=MIDDLE  ALT=\"%28-0.5t%29log%28e+%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=%28-0.5cross%28t%29%29log%28e+%29%2Fcross%28t%29=log%28%281%2Br%29%29 ALIGN=MIDDLE  ALT=\"%28-0.5cross%28t%29%29log%28e+%29%2Fcross%28t%29=log%28%281%2Br%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.5 ALIGN=MIDDLE  ALT=\"-0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   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=%28-1%2F2%29log%28e+%29=log%28%281%2Br%29%29 ALIGN=MIDDLE  ALT=\"%28-1%2F2%29log%28e+%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%28e%5E%28-1%2F2%29+%29=log%28%281%2Br%29%29 ALIGN=MIDDLE  ALT=\"log%28e%5E%28-1%2F2%29+%29=log%28%281%2Br%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....apply exponent rule <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-1%2F2%29=1%2Fe%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"e%5E%28-1%2F2%29=1%2Fe%5E%281%2F2%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%281%2Fe%5E%281%2F2%29+%29=log%28%281%2Br%29%29 ALIGN=MIDDLE  ALT=\"log%281%2Fe%5E%281%2F2%29+%29=log%28%281%2Br%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%281%2F2%29=sqrt%28e%29 ALIGN=MIDDLE  ALT=\"e%5E%281%2F2%29=sqrt%28e%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%281%2Fsqrt%28e%29+%29=log%28%281%2Br%29%29 ALIGN=MIDDLE  ALT=\"log%281%2Fsqrt%28e%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%2Fsqrt%28e%29+=1%2Br ALIGN=MIDDLE  ALT=\"1%2Fsqrt%28e%29+=1%2Br\"   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%2Fsqrt%28e%29+-+1 ALIGN=MIDDLE  ALT=\"r+=+1%2Fsqrt%28e%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "your equation 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;\" > is:<BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+1%2Fsqrt%28e%29+-+1 ALIGN=MIDDLE  ALT=\"r+=+1%2Fsqrt%28e%29+-+1\"   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=4%281%2B1%2Fsqrt%28e%29+-+1%29%5Et ALIGN=MIDDLE  ALT=\"y=4%281%2B1%2Fsqrt%28e%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=4%281%2Fsqrt%28e%29+%29%5Et ALIGN=MIDDLE  ALT=\"y=4%281%2Fsqrt%28e%29+%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4e%5E%28-0.5t%29=4%281%2Fsqrt%28e%29+%29%5Et+ ALIGN=MIDDLE  ALT=\"+4e%5E%28-0.5t%29=4%281%2Fsqrt%28e%29+%29%5Et+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> true\r<BR>\n" );
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document.write( "or \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%281-r%29%5Et ALIGN=MIDDLE  ALT=\"y=4%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=4%281-%281%2Fsqrt%28e%29+-+1%29%29%5Et ALIGN=MIDDLE  ALT=\"y=4%281-%281%2Fsqrt%28e%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=4%281-1%2Fsqrt%28e%29%2B+1%29%5Et ALIGN=MIDDLE  ALT=\"y=4%281-1%2Fsqrt%28e%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=4%282-1%2Fsqrt%28e%29%29%5Et ALIGN=MIDDLE  ALT=\"y=4%282-1%2Fsqrt%28e%29%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4e%5E%28-0.5t%29=4%282-1%2Fsqrt%28e%29%29%5Et ALIGN=MIDDLE  ALT=\"+4e%5E%28-0.5t%29=4%282-1%2Fsqrt%28e%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=4%281%2Fsqrt%28e%29+%29%5Et ALIGN=MIDDLE  ALT=\"y=4%281%2Fsqrt%28e%29+%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );