document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196742>Question 196742</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Suppose that N=  cube-root (x) + 2x + 2 models the number of cases of an infection, in millions, of a disease x years from now. <BR>\n" );
document.write( "a) Approximately how many cases of the infection will there be 16 years from now? <BR>\n" );
document.write( "b) In approximately how many years will there be 7 million cases?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147461 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=147461\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=++x%5E%281%2F3%29+%2B+2x+%2B+2 ALIGN=MIDDLE  ALT=\"N=++x%5E%281%2F3%29+%2B+2x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=+16%5E%281%2F3%29+%2B+16%2A2+%2B+2 ALIGN=MIDDLE  ALT=\"N+=+16%5E%281%2F3%29+%2B+16%2A2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=+2.52+%2B+32+%2B+2 ALIGN=MIDDLE  ALT=\"N+=+2.52+%2B+32+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=+36.52 ALIGN=MIDDLE  ALT=\"N+=+36.52\"   DISABLED_style= \"max-width:90%; height:auto;\" >million\r<BR>\n" );
document.write( "\n" );
document.write( "b) You could solve this algebraically and the plot it OR you could think a little and find the answer emperically (trial and error). In this case, trial and error is quicker.<BR>\n" );
document.write( "Try 1. Then N = 1+2+2 = 5 (not quite 7)<BR>\n" );
document.write( "Try 2. Then N = 1.25+4+2 = 7.25<BR>\n" );
document.write( "So the answer is 'a little less than 2 years'. <BR>\n" );
document.write( "Try 1.9. Then N =   1.23 + 3.8 + 2 = 7.03<BR>\n" );
document.write( "Close enough for me. 1.9 years works :) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );