document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032285>Question 1032285</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Newton’s law of cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. So the rate of cooling for a bottle of lemonade at a room temperature of 75°F which is placed into a refrigerator with temperature of 38°F can be modeled by dT/dt=k(T-38) where T(t) is the temperature of the lemonade after t minutes and T(0) = 75. After 30 minutes the lemonade has cooled to 60°F, so T(30) = 60.<BR>\n" );
document.write( "To the nearest minute, how long does it take for the lemonade to cool to 55°F? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646914 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=646914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The DE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dT%2Fdt=k%28T-38%29+ ALIGN=MIDDLE  ALT=\"dT%2Fdt=k%28T-38%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dT%2F%28T-38%29+=+kdt ALIGN=MIDDLE  ALT=\"dT%2F%28T-38%29+=+kdt\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "==> ln(T-38) = kt + c.\r<BR>\n" );
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document.write( "T(0) = 75 ==> ln37 = c.  ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28%28T-38%29%2F37%29+=+kt ALIGN=MIDDLE  ALT=\"ln%28%28T-38%29%2F37%29+=+kt\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now T(30) = 60 ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28%2860-38%29%2F37%29+=+30k ALIGN=MIDDLE  ALT=\"ln%28%2860-38%29%2F37%29+=+30k\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F30%29ln%2822%2F37%29+=+k ALIGN=MIDDLE  ALT=\"%281%2F30%29ln%2822%2F37%29+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28%28T-38%29%2F37%29+=+%281%2F30%29ln%2822%2F37%29t ALIGN=MIDDLE  ALT=\"ln%28%28T-38%29%2F37%29+=+%281%2F30%29ln%2822%2F37%29t\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28%28T-38%29%2F37%29+=+ln%2822%2F37%29%5E%28t%2F30%29 ALIGN=MIDDLE  ALT=\"ln%28%28T-38%29%2F37%29+=+ln%2822%2F37%29%5E%28t%2F30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28T-38%29%2F37+=+%2822%2F37%29%5E%28t%2F30%29 ALIGN=MIDDLE  ALT=\"%28T-38%29%2F37+=+%2822%2F37%29%5E%28t%2F30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+38%2B37%2A%2822%2F37%29%5E%28t%2F30%29 ALIGN=MIDDLE  ALT=\"T+=+38%2B37%2A%2822%2F37%29%5E%28t%2F30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "To solve for t when T = 55, plug 55 for T into the last equation.<BR>\n" );
document.write( "I will leave the final calculation to you, and you should manage to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t+=+45%29 ALIGN=MIDDLE  ALT=\"highlight%28t+=+45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > minutes, to the nearest minute. </SPAN>\n" );
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