document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176218>Question 1176218</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't know how to do this, please!!\r<BR>\n" );
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document.write( "Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation  dT/dt=k(T−A), where  T is the temperature of the object after t units of time have passed, A is the ambient temperature of the object's surroundings, and  <BR>\n" );
document.write( "k is a constant of proportionality.\r<BR>\n" );
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document.write( "Suppose that a cup of coffee begins at 179 degrees and, after sitting in room temperature of 62 degrees for 11 minutes, the coffee reaches 174 degrees. How long will it take before the coffee reaches 154 degrees?\r<BR>\n" );
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document.write( "Include at least 2 decimal places in your answer.\r<BR>\n" );
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document.write( "= ? minutes<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 #802616 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=802616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The solution to the differential equation is given by:<BR>\n" );
document.write( "T(t) = Ts + (T0 - Ts)exp(-kt), where Ts = the temperature of the surroundings<BR>\n" );
document.write( "T0 = the initial temperature and k = the rate constant<BR>\n" );
document.write( "We can use the information given to solve for k:<BR>\n" );
document.write( "T(11) = 174 = 62 + (179 - 62)exp(-11k)<BR>\n" );
document.write( "exp(-11k) = (174 - 62)/117 -> k = (-1/11)*ln((174 - 62)/117) = 0.0039705<BR>\n" );
document.write( "You can now use this formula to solve for t, if T(t) = 154<BR>\n" );
document.write( "Ans: 60.54 mins </SPAN>\n" );
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