document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201851>Question 201851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Worker Efficiency:  In a study pf worker efficiency at Wong Laboratories it was found that the number of components assembled per hour by the average worker t hours after starting work could be modeled by the formula\r<BR>\n" );
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document.write( "N (t) = -3r3 + 23r2 + 8t\r<BR>\n" );
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document.write( "A. Rewrite the formula by factoring the right-hand side completly<BR>\n" );
document.write( "B. Use the factored version of the formula to find N(3)<BR>\n" );
document.write( "c. Use the accompanying graph to estimate the time at which workers are most efficient.<BR>\n" );
document.write( "d. Use the accompanying graph to estimate the maximum number of components assembled per hour during an 8-hr shift. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152240 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=152240\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Somehow you've got your independent variables a little muddled. I think that the independent variable is t (for time) and not r, as you have it!  So, let's start with...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29+=+-3t%5E3%2B23t%5E2%2B8t ALIGN=MIDDLE  ALT=\"N%28t%29+=+-3t%5E3%2B23t%5E2%2B8t\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this represents the number of components assembled per hour by the average worker t hours after starting work.<BR>\n" );
document.write( "A. The factored form is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29+=+t%283t%2B1%29%28-t%2B8%29 ALIGN=MIDDLE  ALT=\"N%28t%29+=+t%283t%2B1%29%28-t%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B. Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%283%29 ALIGN=MIDDLE  ALT=\"N%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the factored form. Substitute t = 3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%283%29+=+3%283%283%29%2B1%29%28-3%2B8%29 ALIGN=MIDDLE  ALT=\"N%283%29+=+3%283%283%29%2B1%29%28-3%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%283%29+=+3%289%2B1%29%285%29 ALIGN=MIDDLE  ALT=\"N%283%29+=+3%289%2B1%29%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28N%283%29+=+150%29 ALIGN=MIDDLE  ALT=\"highlight%28N%283%29+=+150%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Components per hour 3 hours after starting work.<BR>\n" );
document.write( "The graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29 ALIGN=MIDDLE  ALT=\"N%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C10%2C-5%2C250%2C-3x%5E3%2B23x%5E2%2B8x%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C10%2C-5%2C250%2C-3x%5E3%2B23x%5E2%2B8x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "C. The estimated time, t, at which the workers are most efficient is t = 5, or 5 hours after starting work.<BR>\n" );
document.write( "D. From the graph, it can be estimated that the maximum number of components assembled per hour during an eight-hour shift is 242.<BR>\n" );
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