document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025573>Question 1025573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The current through a particular wire can be modeled by<BR>\n" );
document.write( "I(t) = 2t2 &#8722; 6t + 7\r<BR>\n" );
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document.write( "where I(t) is the current in amperes after t seconds.\r<BR>\n" );
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document.write( "(a) Find the current in the wire after 0.5 seconds.\r<BR>\n" );
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document.write( "The current in the wire after 0.5 seconds would be about_____amperes.\r<BR>\n" );
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document.write( "(b) After how many seconds would the current reach 14 amperes? (Round your answer to two decimal places. Include units with your numerical answers.)<BR>\n" );
document.write( "After about_____the current would reach 14 amperes.\r<BR>\n" );
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document.write( "(c) After how many seconds would the current reach 60 amperes? (Round your answer to two decimal places. Include units with your numerical answers.)<BR>\n" );
document.write( "After about_____the current would reach 60 amperes.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #640865 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=640865\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The current through a particular wire can be modeled by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%28t%29+=+2t%5E2-6t%2B7 ALIGN=MIDDLE  ALT=\"I%28t%29+=+2t%5E2-6t%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%28t%29 ALIGN=MIDDLE  ALT=\"I%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the current in amperes after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds.<BR>\n" );
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document.write( "This is another one of those \"plug-numbers-into-the-equation\" problems.<BR>\n" );
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document.write( "a) Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5 ALIGN=MIDDLE  ALT=\"0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%280.5%29+=+2%2A0.5%5E2-6%2A0.5%2B7=2%2A0.25-3%2B7=0.5-3%2B7=4.5 ALIGN=MIDDLE  ALT=\"I%280.5%29+=+2%2A0.5%5E2-6%2A0.5%2B7=2%2A0.25-3%2B7=0.5-3%2B7=4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The current in the wire after 0.5 seconds would be about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%284.5%29 ALIGN=MIDDLE  ALT=\"highlight%284.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > amperes. <BR>\n" );
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document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%28t%29=14 ALIGN=MIDDLE  ALT=\"I%28t%29=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2-6t%2B7=14 ALIGN=MIDDLE  ALT=\"2t%5E2-6t%2B7=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2-6t%2B7=14 ALIGN=MIDDLE  ALT=\"2t%5E2-6t%2B7=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2-6t%2B7-14=0 ALIGN=MIDDLE  ALT=\"2t%5E2-6t%2B7-14=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2-6t-7=0 ALIGN=MIDDLE  ALT=\"2t%5E2-6t-7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That quadratic equation can be solved by using the quadratic formula or by completing the square.<BR>\n" );
document.write( "The quadratic formula says that the solutions to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (if any)<BR>\n" );
document.write( "are given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In our case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=t%2Ca=2%2Cb=6%2Cc=-7%29 ALIGN=MIDDLE  ALT=\"system%28x=t%2Ca=2%2Cb=6%2Cc=-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so the solution comes from<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%28-6%29+%2B-+sqrt%28%28-6%29%5E2-4%2A2%2A%28-7%29%29%29%2F%282%2A2%29+=+%286+%2B-+sqrt%2836%2B56%29%29%2F4+=+%286+%2B-+sqrt%2892%29%29%2F4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28t=about-0.9%2C%22or%22%2Ct=about3.8979%29 ALIGN=MIDDLE  ALT=\"system%28t=about-0.9%2C%22or%22%2Ct=about3.8979%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The negative value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes no sense, because the problem does not tell us what happens for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%3C0 ALIGN=MIDDLE  ALT=\"t%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >; it is not part of the domain of the function; probably because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0 ALIGN=MIDDLE  ALT=\"t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > was probably the moment the circuit was closed and current started flowing through the wire.<BR>\n" );
document.write( "Rounding the positive answer to two decimal places, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3.90 ALIGN=MIDDLE  ALT=\"t=3.90\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In part (a), we easily included units with your numerical answers, because the units (amperes) were already written for us after the blank space.<BR>\n" );
document.write( "Here it is not so, but we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > is measured in seconds and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%28t%29 ALIGN=MIDDLE  ALT=\"I%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is measured in amperes.<BR>\n" );
document.write( "After about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%223.90+seconds%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%223.90+seconds%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the current would reach 14 amperes. <BR>\n" );
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document.write( "(c) Similarly to what was done for (b), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%28t%29=60 ALIGN=MIDDLE  ALT=\"I%28t%29=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2-6t%2B7=60 ALIGN=MIDDLE  ALT=\"2t%5E2-6t%2B7=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2-6t%2B7=60 ALIGN=MIDDLE  ALT=\"2t%5E2-6t%2B7=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2-6t%2B7-60=0 ALIGN=MIDDLE  ALT=\"2t%5E2-6t%2B7-60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2-6t-53=0 ALIGN=MIDDLE  ALT=\"2t%5E2-6t-53=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Using the quadratic formula,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%28-6%29+%2B-+sqrt%28%28-6%29%5E2-4%2A2%2A%28-53%29%29%29%2F%282%2A2%29+=+%286+%2B-+sqrt%2836%2B424%29%29%2F4+=+%286+%2B-+sqrt%28460%29%29%2F4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The positive solution, rounded to  two decimal places is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=6.86 ALIGN=MIDDLE  ALT=\"t=6.86\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "After about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%226.86+seconds%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%226.86+seconds%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the current would reach 60 amperes.<BR>\n" );
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