document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170670>Question 170670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I did all the math for this one, but still having problems writing out the equation:\r<BR>\n" );
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document.write( "Suppose a population of initial size 100 grows at the rate of 8% per year forever.\r<BR>\n" );
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document.write( "What is the size of the population at the end of year 1? ( 108)\r<BR>\n" );
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document.write( "What is the size of the population at the end of year 2? (117)\r<BR>\n" );
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document.write( "What is the size of the population at the end of year 3? (126)\r<BR>\n" );
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document.write( "(This is where I get lost)\r<BR>\n" );
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document.write( "What is the size of the population at the end of year n (for any integer n)?\r<BR>\n" );
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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 #126004 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=126004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  I did all the math for this one, but still having problems writing out the equation: <BR>\n" );
document.write( "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? ( 108) <BR>\n" );
document.write( "What is the size of the population at the end of year 2? (117) <BR>\n" );
document.write( "What is the size of the population at the end of year 3? (126) <BR>\n" );
document.write( "(This is where I get lost) <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? <BR>\n" );
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document.write( "Use PV = SV*(1 + r)^n where PV is Present Value, SV is Start Value, r is rate and n is periods.  This is common in interest on money, tho the terms used might be different.<BR>\n" );
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document.write( "What is the size of the population at the end of year n (for any integer n)? <BR>\n" );
document.write( "That's the eqn, PV = SV*(1 + r)^n<BR>\n" );
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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? <BR>\n" );
document.write( "The same eqn will do that, PV is 2x SV<BR>\n" );
document.write( "200 = 100*(1 + 0.08)^x<BR>\n" );
document.write( "2 = (1.08)^x<BR>\n" );
document.write( "log(2) = x*log(1.08)<BR>\n" );
document.write( "x = log(2)/log(1.08)<BR>\n" );
document.write( "x =~ 9.006 years<BR>\n" );
document.write( "PS you can use log base 10, or ln, as long as you're consistent.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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