document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106913>Question 1106913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hot drink is taken outside on a cold winter day when the air temperature is &#8722;7°C. According to a principle of physics called Newton's Law of Cooling, the temperature T (in degrees Celsius) of the drink 't' minutes after being taken outside is given by\r<BR>\n" );
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document.write( "T(t) &#8201;=&#8201; &#8722;7 + Ae^(&#8722;kt), \r<BR>\n" );
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document.write( "where A and k are constants.\r<BR>\n" );
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document.write( "(a)<BR>\n" );
document.write( "Suppose that the temperature of the drink is 86°C when it is taken outside. Find the value of the constant A.<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "In addition, suppose that 20 minutes later the drink is 29°C. Find the value of the constant k.<BR>\n" );
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document.write( "What will the temperature be after 28 minutes?<BR>\n" );
document.write( "(d)<BR>\n" );
document.write( "When (i.e., after how many minutes) will the temperature reach 0°C? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721918 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=721918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> T(t) &#8201;=&#8201; &#8722;7 + Ae^(&#8722;kt)<BR>\n" );
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document.write( "(a) t = 0<BR>\n" );
document.write( "86 = -7 + A<BR>\n" );
document.write( "A = 93<BR>\n" );
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document.write( "(b)  29 = -7 + 93 * e^(20k)<BR>\n" );
document.write( "e^(20k) = 36/93 = 0.3871<BR>\n" );
document.write( "20k = ln 0.3871 = &#8722;0.9491<BR>\n" );
document.write( "k = &#8722;0.9491/20 = &#8722;0.0475<BR>\n" );
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document.write( "(c)  T(t) = -7 + 93 * e^(28*&#8722;0.0475) = 17.5964<BR>\n" );
document.write( "after 28 minutes 17.5964 C<BR>\n" );
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document.write( "(d)  0 = -7 + 93 * e^(t*&#8722;0.0475)<BR>\n" );
document.write( " e^(t*&#8722;0.0475) = 7/93 = 0.0753<BR>\n" );
document.write( "t*&#8722;0.0475 = ln 0.0753 = &#8722;2.5863<BR>\n" );
document.write( "t = &#8722;2.5863/&#8722;0.0475 = 54.4484 minutes the drink will be 0C<BR>\n" );
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document.write( " </SPAN>\n" );
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