document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=768201>Question 768201</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The population of the US currently is growing with a doubling time of about 41 years. If the current population is 310 million of people, how many years will it take us to reach a population of 350 million?<BR>\n" );
document.write( "Years to target value (1 decimal): 		 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #468113 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=468113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For now,<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = initial population<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+ ALIGN=MIDDLE  ALT=\"+P+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = current population<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+ ALIGN=MIDDLE  ALT=\"+k+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = years to double population<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+ ALIGN=MIDDLE  ALT=\"+n+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+ ALIGN=MIDDLE  ALT=\"+k+\"   DISABLED_style= \"max-width:90%; height:auto;\" > doubling periods <BR>\n" );
document.write( "it takes to reach target<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Initially,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+0+ ALIGN=MIDDLE  ALT=\"+n+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+a%2A2%5En+ ALIGN=MIDDLE  ALT=\"+P+=+a%2A2%5En+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+a+ ALIGN=MIDDLE  ALT=\"+P+=+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "After <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+ ALIGN=MIDDLE  ALT=\"+k+\"   DISABLED_style= \"max-width:90%; height:auto;\" > years<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+1+ ALIGN=MIDDLE  ALT=\"+n+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+a%2A2%5E1+ ALIGN=MIDDLE  ALT=\"+P+=+a%2A2%5E1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "After <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2k+ ALIGN=MIDDLE  ALT=\"+2k+\"   DISABLED_style= \"max-width:90%; height:auto;\" > years<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+2+ ALIGN=MIDDLE  ALT=\"+n+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+a%2A2%5E2+ ALIGN=MIDDLE  ALT=\"+P+=+a%2A2%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "So, in general, after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%2Ak+ ALIGN=MIDDLE  ALT=\"+n%2Ak+\"   DISABLED_style= \"max-width:90%; height:auto;\" > years,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+a%2A2%5En+ ALIGN=MIDDLE  ALT=\"+P+=+a%2A2%5En+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Now fill in values:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=+41+ ALIGN=MIDDLE  ALT=\"+k+=+41+\"   DISABLED_style= \"max-width:90%; height:auto;\" > years<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+310+ ALIGN=MIDDLE  ALT=\"+a+=+310+\"   DISABLED_style= \"max-width:90%; height:auto;\" > million<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+350+ ALIGN=MIDDLE  ALT=\"+P+=+350+\"   DISABLED_style= \"max-width:90%; height:auto;\" > million<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+350+=+310%2A2%5En+ ALIGN=MIDDLE  ALT=\"+350+=+310%2A2%5En+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5En+=+350%2F310+ ALIGN=MIDDLE  ALT=\"+2%5En+=+350%2F310+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5En+=+1.12903+ ALIGN=MIDDLE  ALT=\"+2%5En+=+1.12903+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the log of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%2Alog%28+2+%29+=+log%28+1.12903+%29%0D%0A%7B%7B%7B+n+=+log%28+1.12903+%29+%2F+log%28+2+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+.05271+%2F+.30103+ ALIGN=MIDDLE  ALT=\"+n+=+.05271+%2F+.30103+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+.1751+ ALIGN=MIDDLE  ALT=\"+n+=+.1751+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%2Ak+=+.1751%2A41+ ALIGN=MIDDLE  ALT=\"+n%2Ak+=+.1751%2A41+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%2Ak+=+7.179+ ALIGN=MIDDLE  ALT=\"+n%2Ak+=+7.179+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In 7.2 years, the population of 350 million will be reached<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+350+=+310%2A2%5En+ ALIGN=MIDDLE  ALT=\"+350+=+310%2A2%5En+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+350+=+310%2A2%5E.1751+ ALIGN=MIDDLE  ALT=\"+350+=+310%2A2%5E.1751+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E.1751+=+35%2F31+ ALIGN=MIDDLE  ALT=\"+2%5E.1751+=+35%2F31+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.12904+=+1.12903+ ALIGN=MIDDLE  ALT=\"+1.12904+=+1.12903+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "close enough\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );