document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044555>Question 1044555</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, this is the question I would love help on:\r<BR>\n" );
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document.write( "A patient suffers from a short fever. Their body temperarure is normally 37.4 degrees celcius but during the fever, it is given by the function:\r<BR>\n" );
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document.write( "y(t) = -0.01t^2 + 0.3e^t + 37.4 (t is greater than or equal to 0)<BR>\n" );
document.write( "where t is the number of hours since the onset of the fever.\r<BR>\n" );
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document.write( "1. What is the average rate of change of temperature y(t) at t=2 and t=6<BR>\n" );
document.write( "2. How fast is the body temperature changing after 3 hours?\r<BR>\n" );
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document.write( "Thank you!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659901 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We need the first derivative of y(t) to give us rate of change<BR>\n" );
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document.write( "y(t) = -0.01t^2 + 0.3e^t + 37.4<BR>\n" );
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document.write( "using the power rule and the fact that the derivative of e^t is e^t<BR>\n" );
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document.write( "y'(t) = 0.3e^t -0.02t<BR>\n" );
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document.write( "y'(2) = 0.3e^2 -0.04 = 0.3(7.39) -0.04 = 2.177 approx 2.18<BR>\n" );
document.write( "y'(6) = 0.3e^6 -0.12 = 120.908 approx 120.91<BR>\n" );
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document.write( "y'(3) = 0.3e^3 -0.06 = 5.965 approx 5.97 <BR>\n" );
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