document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166911>Question 166911</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Not from a textbook.  Not sure how to show or explain the answer.  I can figure out the first 3 years (108, 116.64, 125.97)  I'm not sure about the n and algebraic equation needed.  Thank you in advance for any and all help given.<BR>\n" );
document.write( "Here is the problem.<BR>\n" );
document.write( "Suppose a population of initial size 100 grows at the rate of 8% per year.  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? <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?  Use a calculator to solve to x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123003 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123003\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to find the population at the end of any year, you take 8% of the starting population and add it\r<BR>\n" );
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document.write( "P2=P1+(8%)P1 __ factoring __ P2=P1(1+8%)=P1(1.08)\r<BR>\n" );
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document.write( "P3=P2+(8%)P2 __ factoring __ P3=P2(1+8%)=P2(1.08) __ substituting P3=(P1(1.08))(1.08) __ P3=P1(1.08)^2<BR>\n" );
document.write( "__ 2 is the number of years between P1 and P3\r<BR>\n" );
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document.write( "in general __ Pn=P0(1.08)^n __ where P0 is the original starting population\r<BR>\n" );
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document.write( "200=100(1.08)^n __ dividing by 100 __ 2=1.08^n __ taking log __ log(2)=n(log(1.08))\r<BR>\n" );
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document.write( "dividing by log(1.08) __ (log(2))/(log(1.08))=n __ 9=n (approx)\r<BR>\n" );
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