document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314750>Question 314750</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a population of initial size 100 grows at the rate of 8% per year forever.<BR>\n" );
document.write( "What is the size of the population at the end of year 1?<BR>\n" );
document.write( "What is the size of the population at the end of year 2?<BR>\n" );
document.write( "What is the size of the population at the end of year 3?<BR>\n" );
document.write( "what is the size of the population at the end of year n (for any integer n)?<BR>\n" );
document.write( "What algebraic equation would you need to solve to find the number of years x that it would take for our population to reach 200 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225115 by </B><A HREF=/tutors/aboutme.mpl?userid=Jstrasner><B>Jstrasner(112)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Jstrasner><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=Jstrasner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=225115\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> hey,\r<BR>\n" );
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document.write( "Well the initial equation would be:\r<BR>\n" );
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document.write( "S(size)n=100(1.08^n)\r<BR>\n" );
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document.write( "So for the first year:\r<BR>\n" );
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document.write( "S1= 100(1.08^1)= 108 people<BR>\n" );
document.write( "S2= 100(1.08^2)= 116.64 => so 117 people roughly<BR>\n" );
document.write( "S3= 100(1.08^3)= 125.97 => so 126 people roughly\r<BR>\n" );
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document.write( "As shown above the size at n years is :\r<BR>\n" );
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document.write( "100(1.08^n)\r<BR>\n" );
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document.write( "As for the algebraic equation:\r<BR>\n" );
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document.write( "we would use the one above:\r<BR>\n" );
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document.write( "200 = 100(1.08^n)<BR>\n" );
document.write( "and you would use log\r<BR>\n" );
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document.write( "I hope this helps! </SPAN>\n" );
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