document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122245>Question 122245</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cup of coffee is poured and left to cool on the counter. The formula that represents the temperature of the coffee over time is given by T=80(0.9)^(x/2)+20 where T is temperature in degrees celcius, and x is time in minutes. <BR>\n" );
document.write( "a) What was the initial temperature of the coffee?<BR>\n" );
document.write( "b) How quickly is it cooling?<BR>\n" );
document.write( "c) What is the coolest temperature the coffee will reach? How quickly?<BR>\n" );
document.write( "d) What is the temperature of the coffee after 10 minutes? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89748 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A cup of coffee is poured and left to cool on the counter. The formula that represents the temperature of the coffee over time is given by T=80(0.9)^(x/2)+20 where T is temperature in degrees celcius, and x is time in minutes. <BR>\n" );
document.write( "a) What was the initial temperature of the coffee?<BR>\n" );
document.write( "T(x) = 80(0.9)^(x/2)+20<BR>\n" );
document.write( "T(0) = 80(0.9)^(0/2)+20 = 80*1+20= 100 degrees Celcius.<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "b) How quickly is it cooling?<BR>\n" );
document.write( "T(1) = 80(0.9)^(1/2) 75.89 degrees<BR>\n" );
document.write( "So, in one minute the temperature decreased 24.11 degrees.<BR>\n" );
document.write( "Comment: The decrease is not linear as the function is exponential. <BR>\n" );
document.write( "------------------ <BR>\n" );
document.write( "c) What is the coolest temperature the coffee will reach? Why?<BR>\n" );
document.write( "As x getslarger 0.9^(x/2) gets smaller and smaller.<BR>\n" );
document.write( "To T gets closer and closer to 20 degrees.<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "d) What is the temperature of the coffee after 10 minutes?<BR>\n" );
document.write( "T(10) = 80(0.9)^5 + 20 = 67.2392 degrees Celsius.<BR>\n" );
document.write( "================<BR>\n" );
document.write( "Comment: These termperatures do not look realistic. Coffee at<BR>\n" );
document.write( "100 degrees Celsius would be at the boiling point.<BR>\n" );
document.write( "=============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );