document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176052>Question 1176052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hot bar of iron at 1100 degrees Fahrenheit is quenched in oil at 350 degrees. After 2 minutes, the temperature of the iron is 750 degrees.\r<BR>\n" );
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document.write( "(a) Find the value for k in Newton's Law of Cooling. Round your answer to the nearest thousandth.\r<BR>\n" );
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document.write( "k= ?\r<BR>\n" );
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document.write( "(b) What will the temperature of the iron be after 10 minutes? Round your answer to the nearest degree.\r<BR>\n" );
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document.write( "? degrees Fahrenheit\r<BR>\n" );
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document.write( "(c) How long will it take for the iron to reach 400 degrees? Round your answer to the nearest tenth of a minute.\r<BR>\n" );
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document.write( "? minutes </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #801970 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=801970\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> T(t)=Ts+(To-Ts)*e^(-kt)<BR>\n" );
document.write( "at 2 minutes<BR>\n" );
document.write( "750=350+(1100-350)*e^(-k*2)<BR>\n" );
document.write( "400=750*e^(-2k)<BR>\n" );
document.write( "(8/15)=e^(-2k)<BR>\n" );
document.write( "ln both sides<BR>\n" );
document.write( "-0.6286=-2k<BR>\n" );
document.write( "k=0.3143<BR>\n" );
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document.write( "at 10 minutes e^(-kt)=e^(-3.143)=0.04315<BR>\n" );
document.write( "(750)*0.04315 = 32.36 degrees, so the temperature will be 382 degrees F.<BR>\n" );
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document.write( "at 400 degrees<BR>\n" );
document.write( "400=350+(750*e^(-0.3143t)<BR>\n" );
document.write( "(1/15)=e^(-0.3143t)<BR>\n" );
document.write( "ln both sides\r<BR>\n" );
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document.write( "-2.708=-0.3143t<BR>\n" );
document.write( "t=8.6 minutes.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C20%2C-50%2C1000%2C400%2C350%2B750e%5E%28-0.3143x%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C20%2C-50%2C1000%2C400%2C350%2B750e%5E%28-0.3143x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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