document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=309493>Question 309493</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if the earth's population today is 682,386,000,000 and the growth rate of that population is 2% per year, how long will it take(in years) for the population to increase to 10 times its present value </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #221363 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=221363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the earth's population today is 682,386,000,000 and the growth rate of that population is 2% per year, how long will it take(in years) for the population to increase to 10 times its present value<BR>\n" );
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document.write( "10 = (1 +0.02)^t (t in years)<BR>\n" );
document.write( "1.02^t = 10<BR>\n" );
document.write( "t*log(1.02) = 1<BR>\n" );
document.write( "t = 1/log(1.02)<BR>\n" );
document.write( "t =~ 116.28 years (compounded annually)<BR>\n" );
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document.write( "Population is a continuous process, not just annual adjustments.<BR>\n" );
document.write( "10 = e^rt = e^0.02t<BR>\n" );
document.write( "0.02t = ln(10)<BR>\n" );
document.write( "t = ln(10)/0.02<BR>\n" );
document.write( "t =~ 115.13 years, slightly less<BR>\n" );
document.write( "115.13 years is the correct answer </SPAN>\n" );
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