document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=418067>Question 418067</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A large pond is stocked with fish.The fish population P is modeled by the formula:P=3t+10t^1/2+140, where t is the number  of days since the fish were first introduced into the pond. How many days will it take for the fish population to reach 500? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #292737 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=292737\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A large pond is stocked with fish. The fish population P is modeled by the formula:P=3t+10t^1/2+140,<BR>\n" );
document.write( " where t is the number of days since the fish were first introduced into the pond.<BR>\n" );
document.write( " How many days will it take for the fish population to reach 500?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write the equation:<BR>\n" );
document.write( "3t + 10t^1/2 + 140 = 500<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Subtract 140 from both sides<BR>\n" );
document.write( "3t + 10t^1/2 = 500 - 140<BR>\n" );
document.write( "3t + 10t^1/2 = 360<BR>\n" );
document.write( ";<BR>\n" );
document.write( "We can write this as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3t+%2B+10sqrt%28t%29+=+360+ ALIGN=MIDDLE  ALT=\"3t+%2B+10sqrt%28t%29+=+360+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10sqrt%28t%29+=+360+-+3t+ ALIGN=MIDDLE  ALT=\"10sqrt%28t%29+=+360+-+3t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ";<BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100t+=+%28360-3t%29%5E2 ALIGN=MIDDLE  ALT=\"100t+=+%28360-3t%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100t+=+129600+-+1080t+-+1080t+%2B+9t%5E2 ALIGN=MIDDLE  ALT=\"100t+=+129600+-+1080t+-+1080t+%2B+9t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ";<BR>\n" );
document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( "9t^2 - 2160t - 100t + 129600 = 0<BR>\n" );
document.write( "9t^2 - 2260t + 129600 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "A tiresome equation, use the quadratic formula; a=9, b=-2260, c=129600<BR>\n" );
document.write( "Two solutions, only one is valid<BR>\n" );
document.write( "t = 88.62 days to reach 500 fish<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this in the original equation<BR>\n" );
document.write( "P = 3t + 10t^1/2 + 140<BR>\n" );
document.write( "P = 3(88.62) + 10(88.62^1/2) + 140<BR>\n" );
document.write( "P = 265.86 + 10(9.414) + 140<BR>\n" );
document.write( "P = 265.86 + 94.14 + 140<BR>\n" );
document.write( "P  ~ 500 fish \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );