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 #295895 by </B><A HREF=/tutors/aboutme.mpl?userid=Gersid><B>Gersid(33)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Gersid><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=295895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a problem in exponential decay for which you can use the exponential function: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ab%5Ex ALIGN=MIDDLE  ALT=\"y+=+ab%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where the base, b, is between 0 and 1 for exponential decay. x is the number of years given in the problem (x = 8).<BR>\n" );
document.write( "Start with the exponential function:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ab%5Ex ALIGN=MIDDLE  ALT=\"y+=+ab%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute y = 450, the current number of owls. a = 12,000, the number of owls 8 years ago, and x = 8.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=450+=+%2812000%29b%5E8 ALIGN=MIDDLE  ALT=\"450+=+%2812000%29b%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solving for b will give you the exponential function for this situation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E8+=+450%2F12000 ALIGN=MIDDLE  ALT=\"b%5E8+=+450%2F12000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use your calculator to take the eighth root of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+0.6634 ALIGN=MIDDLE  ALT=\"b+=+0.6634\"   DISABLED_style= \"max-width:90%; height:auto;\" > Approx. Now you can write the exponential function for this situation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+12000%280.6634%29%5Ex ALIGN=MIDDLE  ALT=\"y+=+12000%280.6634%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The question you want to answer is - For what value of x (x = number of years) will y (the number of owls remaining) = 1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+12000%280.6634%29%5Ex ALIGN=MIDDLE  ALT=\"1+=+12000%280.6634%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for x. Divide both sides by 12000.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12000+=+%280.6634%29%5Ex ALIGN=MIDDLE  ALT=\"1%2F12000+=+%280.6634%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the logarithm of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%281%2F12000%29+=+xLog%280.6634%29 ALIGN=MIDDLE  ALT=\"Log%281%2F12000%29+=+xLog%280.6634%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > From the power rule for logarithms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+Log%281%2F12000%29%2FLog%280.6634%29 ALIGN=MIDDLE  ALT=\"x+=+Log%281%2F12000%29%2FLog%280.6634%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use your calculator to evaluate.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+22.8878 ALIGN=MIDDLE  ALT=\"x+=+22.8878\"   DISABLED_style= \"max-width:90%; height:auto;\" > years.<BR>\n" );
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