document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138860>Question 1138860</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question with exponential functions \r<BR>\n" );
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document.write( "A cup of hot liquid was left to cool in a room whose temperature was 18°C. The temperature changes according to the function T(t)=80(1/2)^t/30)+18<BR>\n" );
document.write( "What are the y-intercept and the equation of the horizontal asymptote?  What do they mean in this context?\r<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 #756666 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756666\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the room temperature is 18 degrees centigrade.\r<BR>\n" );
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document.write( "the temperature changes according to the function T(t) = 80 * (1/2)^(t/30) + 18.\r<BR>\n" );
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document.write( "the y intercept is really the T(t) intercept in this equation.\r<BR>\n" );
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document.write( "that's the value of T(t) when t = 0.\r<BR>\n" );
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document.write( "in the context of this problem, that would be the temperature of the hot liquid when it is first placed in the room.\r<BR>\n" );
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document.write( "as t gets larger, the temperature changes according to the formula.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "when t = 0, the temperature of the liquid is 98 degrees.<BR>\n" );
document.write( "when t = 50, the temperature of the liquid is 43.198 degrees.<BR>\n" );
document.write( "when t = 100, the temperature of the liquid is 25.937 degrees.<BR>\n" );
document.write( "when t = 200, the temperature of the liquid is 18.787 degrees.<BR>\n" );
document.write( "when t = 300, the temperature of the liquid is 18.078 degrees.<BR>\n" );
document.write( "when t = 500, the temperature of the liquid is 18.001 degrees.\r<BR>\n" );
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document.write( "the temperature of the liquid will never go below 18 degrees centigrade because that's the temperature of the room.\r<BR>\n" );
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document.write( "the graph of the equation is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/041131.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "in the graph, i let y = T(t) and i let x = t.\r<BR>\n" );
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document.write( "as x gets larger, (1/2) ^ (x/30) gets smaller until it approaches 0\r<BR>\n" );
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document.write( "as it approaches 0, the temperature of the liquid approaches 18 degrees centigrade which is the temperature of the room.\r<BR>\n" );
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document.write( "to summarize.\r<BR>\n" );
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document.write( "when t = 0, that's the temperature of the liquid as it is placed in the room.\r<BR>\n" );
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document.write( "as t gets larger, the temperature of the liquid approaches 18 degrees centigrade and will never get lower than that.\r<BR>\n" );
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