document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1068258>Question 1068258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Discrete mathematics.<BR>\n" );
document.write( "A colony of bats is counted every 2 months. The first four counts are 1200, 1800, 2700, and 4050.<BR>\n" );
document.write( "a. Assuming that this growth rate continues, write a recurrence relation for the number of bats at count n.<BR>\n" );
document.write( "b. Solve the recurrence relation.<BR>\n" );
document.write( "c. What will the 12th count be? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #683476 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=683476\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> start with 1200<BR>\n" );
document.write( "next is 1800 which is 1.5 * 1200.<BR>\n" );
document.write( "next is 2700 which is 1.5 * 1800.<BR>\n" );
document.write( "next is 4050 which is 1.5 * 2700.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it looks like the population of bats is increasing 1.5 times every 2 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula would be b.n = b.0 * 1.5 ^ n\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b.n is the future population.<BR>\n" );
document.write( "b.0 is the present population of bats which is 1200.<BR>\n" );
document.write( "1.5 is the growth factor every 2 months.<BR>\n" );
document.write( "n is the number of 2 month periods.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "using this formula, you get the following:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "after 1 two month period, the population is 1200 * 1.5 = 1800.<BR>\n" );
document.write( "after 2 two month periods, the population is 1200 * 1.5 ^ 2 = 2700.<BR>\n" );
document.write( "after 3 two month periods, the population is 1200 * 1.5 ^ 3 = 4050.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "after 12 two month periods, the population is 1200 * 1.5 ^ 12 = 155,695.6055.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is not the recurrence formula, or what might be called a recursive formula, however.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the recurrence formula would be, to the best of my knowledge, b.(n+1) = b.n * 1.5, where b.0 is equal to 1200.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so you start with b.0 = 1200<BR>\n" );
document.write( "b.(n+1) = b.n * 1.5 becomes b.1 = b.0 * 1.5 which gets you b.1 = 1200 * 1.5 = 1800<BR>\n" );
document.write( "b.(n+1) = b.n * 1.5 then becomes b.2 = b.1 * 1.5 which gets you b.2 = 1800 * 1.5 = 2700.<BR>\n" );
document.write( "each succeeding time period results in a bat population which is 1.5 times the previous time period.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the succession becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b.0 = 1200<BR>\n" );
document.write( "b.1 = 1800<BR>\n" );
document.write( "b.2 = 2700<BR>\n" );
document.write( "b.3 = 4050<BR>\n" );
document.write( "b.4 = 6075<BR>\n" );
document.write( "b.5 = 9112.5<BR>\n" );
document.write( "b.6 = 13,668.75<BR>\n" );
document.write( "b.7 = 20,503.125<BR>\n" );
document.write( "b.8 = 30,754.6875<BR>\n" );
document.write( "b.90 = 46,132.03125<BR>\n" );
document.write( "b.10 = 69,198.04688<BR>\n" );
document.write( "b.11 = 103,797.0703<BR>\n" );
document.write( "b.12 = 155,695.6055\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "note that b.n means b sub n which means the nth occurrence of the 2 month growth periods.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you start with b.0 which is equal to 1200.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "next is b.1 which is 1.5 * 1200 which is equal to 1800.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i used the b to indicate the number of bats in the nth growth period.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );