document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150537>Question 150537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a bird species in danger of extinction has a population that is decreasing (A=A(base0)e^kt). five years ago the population was at 1400 and today only 1000 are still alive. once the population drops below 100, the situation is irreversible. When will this happen? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110500 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=110500\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a bird species in danger of extinction has a population that is decreasing (A=A(base0)e^kt). five years ago the population was at 1400 and today only 1000 are still alive. once the population drops below 100, the situation is irreversible. When will this happen?<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "A(t) = A(o) e^(kt)<BR>\n" );
document.write( "Find \"k\":<BR>\n" );
document.write( "1000 = 1400 e^(k*5)<BR>\n" );
document.write( "(5/7) = e^(5k)<BR>\n" );
document.write( "Take the ln to get:<BR>\n" );
document.write( "5k = ln (5/7)<BR>\n" );
document.write( "5k = -0.3365<BR>\n" );
document.write( "k = -0.06729<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Equation: A(t) = A(o) e^(-0.06729t)<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "When will the population be 100?<BR>\n" );
document.write( "100 = 1000 e^(-0.06729t)<BR>\n" );
document.write( "0.10 = e^(-0.06729t)<BR>\n" );
document.write( "-0.06729t = ln(0.10)<BR>\n" );
document.write( "t = 31.22 years from 5 yrs. ago <BR>\n" );
document.write( "OR<BR>\n" );
document.write( "26.22 years from NOW<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );