document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147814>Question 147814</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the function P=12+50ln x represents the percentage of inbound e-mail in the U.S. that is considered spam, where x is the number of years after 2001.\r<BR>\n" );
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document.write( "Carry all calculations to six decimals on each intermediate step when necessary.<BR>\n" );
document.write( "a) use this model to approximate the percentage of spam in the year 2005. I need to know all steps please.\r<BR>\n" );
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document.write( "b) Use this model to determine how many years it will take (to two decimal places) for the percent of spam to reach 90% provided that the law enforcement regarding spammers does not change. <BR>\n" );
document.write( "My answer fo first part is P=12+3.91(4) =   P=12+15.65  P= 27.65%  Is this correct and the second part  90=12+50ln(x),  90=12+3.91(x),   90=15.91x,  15.91years  Is this correct?   Thanks for help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108270 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=108270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your thinking is correct.<BR>\n" );
document.write( "However your calculations are not.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=12%2B50%2Aln%28x%29 ALIGN=MIDDLE  ALT=\"P=12%2B50%2Aln%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=12%2B50%2Aln%284%29 ALIGN=MIDDLE  ALT=\"P=12%2B50%2Aln%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=12%2B50%2A1.386294 ALIGN=MIDDLE  ALT=\"P=12%2B50%2A1.386294\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'm not sure where the 3.91 comes in other than from ln(50)=3.91.<BR>\n" );
document.write( "That's your mistake. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=12%2B50%2A1.386294 ALIGN=MIDDLE  ALT=\"P=12%2B50%2A1.386294\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=12%2B69.31 ALIGN=MIDDLE  ALT=\"P=12%2B69.31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=81.31 ALIGN=MIDDLE  ALT=\"P=81.31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And the same for the second part.<BR>\n" );
document.write( "The thinking was clear but the calculation had mistakes. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90=12%2B50%2Aln%28x%29 ALIGN=MIDDLE  ALT=\"90=12%2B50%2Aln%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=78=50%2Aln%28x%29 ALIGN=MIDDLE  ALT=\"78=50%2Aln%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 12 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.56=ln%28x%29 ALIGN=MIDDLE  ALT=\"1.56=ln%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both side by 50.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4.76 ALIGN=MIDDLE  ALT=\"x=4.76\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the inverse of the natural log function (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( " </SPAN>\n" );
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