document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=953768>Question 953768</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'd like some explanation this question please:\r<BR>\n" );
document.write( "\n" );
document.write( "3. A population of rats grows at a rate which is proportional to the number of rats, y, existing at the end of month t.  Initially there are 50 rats, and after 2 months there are 100 rats.\r<BR>\n" );
document.write( "\n" );
document.write( "(i)  Find a relationship between y and t. <BR>\n" );
document.write( "(given answer --> y = 50(sqrt(2))^t)\r<BR>\n" );
document.write( "\n" );
document.write( "(ii) Find the number of rats present after 1 year.  (given answer --> 3200)\r<BR>\n" );
document.write( "\n" );
document.write( "My answer to (i) is different but still gives the correct values for 2 months and 12 months:\r<BR>\n" );
document.write( "\n" );
document.write( "y= exp ( (ln2)/2 * t + ln50)\r<BR>\n" );
document.write( "\n" );
document.write( "Obviously mine is much less elegant, but I can't see how the given answer is arrived at.\r<BR>\n" );
document.write( "\n" );
document.write( "My equation is derived from:\r<BR>\n" );
document.write( "\n" );
document.write( "dy/dt = ky\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks, \r<BR>\n" );
document.write( "\n" );
document.write( "Robert </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #582511 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=582511\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We can solve this using the constant of proportionality, k<BR>\n" );
document.write( "we are given,<BR>\n" );
document.write( "y = 50*k^t and y = 50 for t = 0, hence t is the exponent of k<BR>\n" );
document.write( "100 = 50*k^2 and y = 100 for t = 2, then<BR>\n" );
document.write( "k^2 = 2<BR>\n" );
document.write( "k = square root (2)<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "y = 50 *(square root(2)^t)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );