document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=585462>Question 585462</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of fish in a lake is decreasing. There are currently 24,000 fish in the lake. The population is decreasing 6% each year. In how many years will there be 1/4 of the current number of the fish in the lake? Use formula T(n)=a(1+r)^n to solve problem?\r<BR>\n" );
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document.write( "-please someone help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #373356 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=373356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> T(n)=a(1+r)^n\r<BR>\n" );
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document.write( "T(n)=24000(1+(-0.06))^n\r<BR>\n" );
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document.write( "T(n)=24000(1-0.06)^n\r<BR>\n" );
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document.write( "T(n)=24000(0.94)^n\r<BR>\n" );
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document.write( "So the formula is T(n)=24000(0.94)^n \r<BR>\n" );
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document.write( "Now plug in T(n) = 24000/4 = 6000 and solve for n\r<BR>\n" );
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document.write( "T(n)=24000(0.94)^n\r<BR>\n" );
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document.write( "6000=24000(0.94)^n\r<BR>\n" );
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document.write( "6000/24000=(0.94)^n\r<BR>\n" );
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document.write( "1/4=(0.94)^n\r<BR>\n" );
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document.write( "ln(1/4) = ln((0.94)^n)\r<BR>\n" );
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document.write( "ln(1/4) = n*ln(0.94)\r<BR>\n" );
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document.write( "ln(1/4)/ln(0.94) = n\r<BR>\n" );
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document.write( "n = ln(1/4)/ln(0.94)\r<BR>\n" );
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document.write( "n = 22.4046\r<BR>\n" );
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document.write( "So in roughly 22.4046 years, the population will be 1/4 of the current population.\r<BR>\n" );
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document.write( "Jim<BR>\n" );
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