document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176776>Question 176776</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? 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 #131848 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=131848\">put this solution on YOUR website!</A><BR><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( "100*(1.08)<BR>\n" );
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document.write( "What is the size of the population at the end of year 2?<BR>\n" );
document.write( "100(1.08)^2<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "What is the size of the population at the end of year 3?<BR>\n" );
document.write( "100(1.08)^3<BR>\n" );
document.write( "----------------------------<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( "100(1.08)^n<BR>\n" );
document.write( "-----------------------<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.<BR>\n" );
document.write( "100(1.08)^n = 200 <BR>\n" );
document.write( "1.08^n = 2<BR>\n" );
document.write( "n = log(2)/log(1.08) = 9.0064 years<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );