document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=968704>Question 968704</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the absence of predators, the natural growth rate of rabbits is<BR>\n" );
document.write( "4% per year. A population begins with 100 rabbits. The function<BR>\n" );
document.write( "f(x) = 100(1.04)^x gives the population of rabbits in x years.<BR>\n" );
document.write( "a. How long will it take the population of rabbits to double? <BR>\n" );
document.write( "b.  How long will it take the population of rabbits to reach 1000?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591908 by </B><A HREF=/tutors/aboutme.mpl?userid=amarjeeth123><B>amarjeeth123(570)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=amarjeeth123><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=591908\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a.For the population to double we have 100(1.04)^x=200<BR>\n" );
document.write( "  (1.04)^x=2<BR>\n" );
document.write( "  Taking logarithm on both sides to base 10 we get,<BR>\n" );
document.write( "  x log(1.04)=log2<BR>\n" );
document.write( "  x=log2/log(1.04)=17.67 years<BR>\n" );
document.write( " It will double in 17.67 years.<BR>\n" );
document.write( "b.For the population to become 1000 we have 100(1.04)^x=1000<BR>\n" );
document.write( "  (1.04)^x=10<BR>\n" );
document.write( "  Taking logarithm on both sides to base 10 we get,<BR>\n" );
document.write( "  x log(1.04)=log 10<BR>\n" );
document.write( "  x log(1.04)=1<BR>\n" );
document.write( "  x=1/log(1.04)=58.708 years.<BR>\n" );
document.write( "  It will become 1000 in 58.708 years. </SPAN>\n" );
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