document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=137588>Question 137588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do i work out a problem when given \r<BR>\n" );
document.write( "\n" );
document.write( "How long will it take for the population of a certain country to double<BR>\n" );
document.write( "if its annual growth rate is 5 percent? \r<BR>\n" );
document.write( "\n" );
document.write( "First I plugged in 5 (for 5%)  Log in my calculatorand the answer was 0.l698970004. <BR>\n" );
document.write( " Do i move the decimal over 2 places to give me 16.989 years or <BR>\n" );
document.write( "rather that it would take 17 years for the population to double. <BR>\n" );
document.write( " I have researched everthing and am unable to come up with any samples on how to work out any problems given just the percent without a population number?  Can you please help me understand how to do this? <BR>\n" );
document.write( "  Is it just a calculator problem? <BR>\n" );
document.write( "Any help would be greatly appreciated. <BR>\n" );
document.write( "Thank You.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #100641 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=100641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem is in your base. <BR>\n" );
document.write( "You are not using base 10.<BR>\n" );
document.write( "Here's the equation that describes your problem.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29=N%5B0%5D%281.05%29%5Et ALIGN=MIDDLE  ALT=\"N%28t%29=N%5B0%5D%281.05%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At time t=0, your population is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%5B0%5D ALIGN=MIDDLE  ALT=\"N%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "You're looking for t when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29=2%2AN%5B0%5D ALIGN=MIDDLE  ALT=\"N%28t%29=2%2AN%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2AN%5B0%5D=N%5B0%5D%281.05%29%5Et ALIGN=MIDDLE  ALT=\"2%2AN%5B0%5D=N%5B0%5D%281.05%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=%281.05%29%5Et ALIGN=MIDDLE  ALT=\"2=%281.05%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The base for your logarithm is 1.05. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%281.05%2C2%29=t ALIGN=MIDDLE  ALT=\"log%281.05%2C2%29=t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can transform that into a base 10 problem with a substitution.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=log%2810%2C2%29%2Flog%2810%2C1.05%29 ALIGN=MIDDLE  ALT=\"t=log%2810%2C2%29%2Flog%2810%2C1.05%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0.30103%2F.021189%29 ALIGN=MIDDLE  ALT=\"t=0.30103%2F.021189%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=14.2067%29 ALIGN=MIDDLE  ALT=\"t=14.2067%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The time to double is 14.2067 years. <BR>\n" );
document.write( "Checking the answer, you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29=2N%5B0%5D ALIGN=MIDDLE  ALT=\"N%28t%29=2N%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );