document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042099>Question 1042099</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The amount of active ingredient of medicine ingested by the body, A in milligrams, is a function of time, t, in hours, given by A(t)=5/8(12t-t^2). <BR>\n" );
document.write( "a)Determine the average rate of change of the amount of medicine ingested during each of the intervals below and compare the two rates with resect to the given situation. <BR>\n" );
document.write( "4 to 6 hours and 6 to 8 hours. <BR>\n" );
document.write( "b) Estimate the slope of the tangent at the point P(4,80/3). Use interval of 0.01. Round final answer to the nearest hundredth. Explain what the value represents for this situation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #657029 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=657029\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The amount of active ingredient of medicine ingested by the body, A in milligrams, is a function of time, t, in hours, given by A(t)=5/8(12t-t^2). <BR>\n" );
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document.write( "a)Determine the average rate of change of the amount of medicine ingested during each of the intervals below and compare the two rates with respect to the given situation. <BR>\n" );
document.write( "4 to 6 hours and 6 to 8 hours.<BR>\n" );
document.write( "A(4) = (5/8)(48-16) = 160/8<BR>\n" );
document.write( "A(6) = (5/8)(72-36) = 180/8<BR>\n" );
document.write( "A(8) = (5/8)(96-64) = 160/8<BR>\n" );
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document.write( "rate from 4 to 6 hrs:: (180/8-160/8)/2 = 20/16 = 5/4 = 1.25 ml per hr <BR>\n" );
document.write( "That means the rate at which the medicine is ingested is increasing.<BR>\n" );
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document.write( "rate from 6 to 8 hrs:: (160/8-180/8)/2 = -1.25 ml per hr<BR>\n" );
document.write( "That means the rate at which the medicine is ingested is decreasing.<BR>\n" );
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document.write( "b) Estimate the slope of the tangent at the point P(4,80/3). Use interval of 0.01. Round final answer to the nearest hundredth. Explain what the value represents for this situation.<BR>\n" );
document.write( "Note: (4,80/3) is not a point of the function; (4,20) is a point of the function.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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