document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=581319>Question 581319</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the function : P=15+40*ln(x)  represents the percentage of inbound <BR>\n" );
document.write( "e-mail in the U.S. that is considered spam, where x is the number of years after 2002. <BR>\n" );
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 2006 to the <BR>\n" );
document.write( "nearest tenth of a percent.  <BR>\n" );
document.write( "b) Use this model to determine in how many years it will take for the percent of <BR>\n" );
document.write( "spam to reach 90% provided that law enforcement regarding spammers does not <BR>\n" );
document.write( "change.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371569 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=371569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose that the function : P=15+40*ln(x) represents the percentage of inbound<BR>\n" );
document.write( "e-mail in the U.S. that is considered spam, where x is the number of years after 2002.<BR>\n" );
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 2006 to the<BR>\n" );
document.write( "nearest tenth of a percent.<BR>\n" );
document.write( "x = 2006-2002 = 4<BR>\n" );
document.write( "plug that into:<BR>\n" );
document.write( "P=15+40*ln(x)<BR>\n" );
document.write( "P=15+40*ln(4)<BR>\n" );
document.write( "P=15+40*1.3863<BR>\n" );
document.write( "P=15+55.4518<BR>\n" );
document.write( "P=70.5%<BR>\n" );
document.write( "b) Use this model to determine in how many years it will take for the percent of<BR>\n" );
document.write( "spam to reach 90% provided that law enforcement regarding spammers does not<BR>\n" );
document.write( "change.<BR>\n" );
document.write( "Set p to 90 and solve for x:<BR>\n" );
document.write( "P=15+40*ln(x)<BR>\n" );
document.write( "90=15+40*ln(x)<BR>\n" );
document.write( "75=40*ln(x)<BR>\n" );
document.write( "1.875 = ln(x)<BR>\n" );
document.write( "e^1.875 = x<BR>\n" );
document.write( "6.52 years = x\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );