document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=424440>Question 424440</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please. could you explain in details for this college algebra problem?\r<BR>\n" );
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document.write( "The population of a certain endangered species of owl is declining exponentially. There are currently 450 living specimens, whereas just 8 years ago there were 12,000 . If the population continues to decline exponentially, how long will it be until there is only a single owl left?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #295892 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=295892\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The population of a certain endangered species of owl is declining exponentially. There are currently 450 living specimens, whereas just 8 years ago there were 12,000 . If the population continues to decline exponentially, how long will it be until there is only a single owl left?<BR>\n" );
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document.write( "apply exponential equation:<BR>\n" );
document.write( "y = xe^(kt)<BR>\n" );
document.write( "where<BR>\n" );
document.write( "y is amount after time t<BR>\n" );
document.write( "x is initial amount<BR>\n" );
document.write( "k is a constant<BR>\n" );
document.write( "t is time<BR>\n" );
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document.write( "plug in all given data to find k:<BR>\n" );
document.write( "450 = 12000e^(8k)<BR>\n" );
document.write( "450/12000 = e^(8k)<BR>\n" );
document.write( "ln(450/12000) = 8k<BR>\n" );
document.write( "ln(450/12000)/8 = k<BR>\n" );
document.write( "-0.41043 = k<BR>\n" );
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document.write( "Our general equation is:<BR>\n" );
document.write( "y = 12000e^(-0.41043t)<BR>\n" );
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document.write( "we now set y to 1 and solve for t:<BR>\n" );
document.write( "1 = 12000e^(-0.41043t)<BR>\n" );
document.write( "1/12000 = e^(-0.41043t)<BR>\n" );
document.write( "ln(1/12000) = -0.41043t<BR>\n" );
document.write( "ln(1/12000)/(-0.41043) = t<BR>\n" );
document.write( "22.89 years = t\r<BR>\n" );
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