document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=59515>Question 59515</A>: <I><SPAN STYLE=\"word-break: break-all;\"> S. Bones is the doctor in Deathly, Ill., a suburb of Chicago. One day, John Garfinkle comes in with a high fever. Dr. Bones takes a blood sample and finds that it contains 1300 flu viruses per cubic millimeter and is increasing. John immediately gets a shot pf penicillin. The virus count should continue to increase for a while, then (hopefully!) level off and go back down. After 5 minutes the virus count is up to 1875, and after 5 more minutes, it is 2400. Assume the virus count varies quadratically with the number of minutes since the shot.\r<BR>\n" );
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document.write( "Find the equation expressing the number of viruses per cubic millimeter in terms of the number of minutes since the shot. Be sure to define your variables, set up a system of equations and use matrices to solve. Show all steps.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41441 by </B><A HREF=/tutors/aboutme.mpl?userid=hayek><B>hayek(51)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=hayek><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=41441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> t=0: 1300 flu/cc<BR>\n" );
document.write( "t=+5min: 1875 flu/cc<BR>\n" );
document.write( "t=+10min: 2400 flu/cc\r<BR>\n" );
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document.write( "The problem tells us \"the virus count varies quadratically with the number of minutes since the shot\", so it is in this form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=virus=a%2At%5E2%2Bb%2At%2Bc ALIGN=MIDDLE  ALT=\"virus=a%2At%5E2%2Bb%2At%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Let's plug in the data we have in order to solve for a, b and c:<BR>\n" );
document.write( "Eq.1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=a%2A0%5E2%2Bb%2A0%2Bc=1300 ALIGN=MIDDLE  ALT=\"f%280%29=a%2A0%5E2%2Bb%2A0%2Bc=1300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Eq.2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29=a%2A5%5E2%2Bb%2A5%2Bc=1875 ALIGN=MIDDLE  ALT=\"f%285%29=a%2A5%5E2%2Bb%2A5%2Bc=1875\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Eq.3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2810%29=a%2A10%5E2%2Bb%2A10%2Bc=2400 ALIGN=MIDDLE  ALT=\"f%2810%29=a%2A10%5E2%2Bb%2A10%2Bc=2400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----<BR>\n" );
document.write( "Eq. 1 ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=1300%29 ALIGN=MIDDLE  ALT=\"highlight%28c=1300%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------<BR>\n" );
document.write( "Plug that result into Eq.2: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25a%2B5b%2B1300=1875 ALIGN=MIDDLE  ALT=\"25a%2B5b%2B1300=1875\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then solve for a:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25a=575-5b ALIGN=MIDDLE  ALT=\"25a=575-5b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Eq. 4: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28115-b%29%2F5 ALIGN=MIDDLE  ALT=\"a=%28115-b%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Now, plug that result into Eq.3:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2A%28115-b%29%2F5%2B10b%2B1300=2400 ALIGN=MIDDLE  ALT=\"100%2A%28115-b%29%2F5%2B10b%2B1300=2400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2300-20b%2B10b=1100 ALIGN=MIDDLE  ALT=\"2300-20b%2B10b=1100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10b=-1200 ALIGN=MIDDLE  ALT=\"-10b=-1200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=120%29 ALIGN=MIDDLE  ALT=\"highlight%28b=120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Using that result in Eq. 4, we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28115-120%29%2F5 ALIGN=MIDDLE  ALT=\"a=%28115-120%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=-1%29 ALIGN=MIDDLE  ALT=\"highlight%28a=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------<BR>\n" );
document.write( "So the formula for virus count in terms of time in minutes is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28virus%28t%29=-t%5E2%2B120%2At%2B1300%29 ALIGN=MIDDLE  ALT=\"highlight%28virus%28t%29=-t%5E2%2B120%2At%2B1300%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "You can plug in the data to check that the formula is correct.\r<BR>\n" );
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document.write( "Here is a graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-80%2C200%2C-6000%2C6000%2C-x%5E2%2B120%2Ax%2B1300%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-80%2C200%2C-6000%2C6000%2C-x%5E2%2B120%2Ax%2B1300%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );