document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192107>Question 192107</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 #144145 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=144145\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A=P(1+r)^t\r<BR>\n" );
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document.write( "1)   A(1) = 100(1.08)^1= 108<BR>\n" );
document.write( "2)  A(2)=  100(1.08)^2=116.64<BR>\n" );
document.write( "3) A(3)= 100(1.08)^3=125.97<BR>\n" );
document.write( "4) A(n)=100(1.08)^n<BR>\n" );
document.write( "5)  200=100(1.08)^n<BR>\n" );
document.write( "divide  both  sides  by  100<BR>\n" );
document.write( "2=(1.08)^n\r<BR>\n" );
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document.write( "log  both  sides\r<BR>\n" );
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document.write( "log2 =log (1.08)^n=n*log(1.08)\r<BR>\n" );
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document.write( "divide  both  sides  by  log(1.08)  and  simplify\r<BR>\n" );
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document.write( "(log(2))/(log(1.08))= 9.006=n\r<BR>\n" );
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document.write( "check<BR>\n" );
document.write( "200=100log(1.08)^9.006=  200     ok </SPAN>\n" );
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