document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=179110>Question 179110</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The fish population in a certain lake rises and falls accourding to the formula:<BR>\n" );
document.write( "F=1000(30+15t-t^2)\r<BR>\n" );
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document.write( "Here, F is the number of fish at t, time, where t is measured in years since January 1,2002.\r<BR>\n" );
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document.write( "When will the fish population be the same as it was on January 1,2002?\r<BR>\n" );
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document.write( "All of the fish will die after approximately t=? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134057 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=134057\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The fish population in a certain lake rises and falls accourding to the formula:<BR>\n" );
document.write( "F=1000(30+15t-t^2) <BR>\n" );
document.write( "Here, F is the number of fish at t, time, where t is measured in years since January 1,2002. <BR>\n" );
document.write( "When will the fish population be the same as it was on January 1,2002? <BR>\n" );
document.write( "---<BR>\n" );
document.write( "In 2002, t = 0<BR>\n" );
document.write( "Then F = 1000(30 + 15*0-0^2) = 30,000<BR>\n" );
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document.write( "Solve F=30,000 for another value of \"t\":<BR>\n" );
document.write( "1000(30+15t-t^2) = 30000<BR>\n" );
document.write( "Rearrange:-t^2 + 15t + 30 = 30<BR>\n" );
document.write( "-t^2+15t = 0<BR>\n" );
document.write( "-t(t-15) = 0<BR>\n" );
document.write( "t = 0 or t=15<BR>\n" );
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document.write( "Year?  2002 + 15 = 2017<BR>\n" );
document.write( "There will be 30,000 fish in 2017<BR>\n" );
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document.write( "All of the fish will die after approximately t=?<BR>\n" );
document.write( "F=1000(30+15t-t^2)<BR>\n" );
document.write( "Let F=0 and solve for \"t\"<BR>\n" );
document.write( "1000(30+15t-t^2) = 0<BR>\n" );
document.write( "30 + 15t -t^2 = 0 <BR>\n" );
document.write( "t^2 - 15t -30 = 0<BR>\n" );
document.write( "t = [15 +- sqrt(225 - 4*-30)]/2\r<BR>\n" );
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document.write( "t = [15 +- sqrt(355)]/2<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( "t = 16.92<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "No fish in 2002 + 16.92 = 2019<BR>\n" );
document.write( "=======================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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