Average Temperature

<BODY LANG="EN" > <HR><center> <table border=1> <td><A HREF="node70.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="node70.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node72.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node71.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </table> </center> <HR> <H3>Average Temperature</H3> <P> The average daily temperature <I>T</I> (in Fahrenheit) of Yourtown, USA, is estimated by the function <P> <CENTER> <IMG WIDTH=219 HEIGHT=39 ALIGN=BOTTOM ALT="[T formula]" SRC="img210.gif"> </CENTER> <P> where <I>t</I> is measured in days and <I>t</I>=1 is the first day of the year, while <I>t</I>=365 is New Year's Eve. Find the average daily temperature of Yourtown on Christmas Eve. <P> Before actually doing the problem, I would like for you to think about a few secondary questions. What is the period of this function? What roles do the 62, 20, and 35 play here? And, finally, crucial to solving the problem, what is <I>t</I> on Christmas Eve? <P> Back to the problem at hand. First, we note that Christmas Eve, December 24, corresponds to the 358th day of our calendar year (assuming it is not a leap year). Hence, for our problem, <I>t</I>=358. Now, to find the average temperature on this day, we simply plug <I>t</I>=358 into the function for <I>T</I>. This yields <P> <CENTER> <IMG WIDTH=369 HEIGHT=155 ALIGN=BOTTOM ALT="eqnarray678" SRC="img211.gif"> </CENTER> <P> <P> Thus, we see that our model approximates the temperature on Christmas Eve by the value <I>T</I>=47.004 degrees Fahrenheit. <P> <HR><center> <table border=1> <td><A HREF="node70.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="node70.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node72.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node71.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </table> </center> <HR><P><ADDRESS> <I><A HREF="http://www.math.psu.edu/sellersj/">James A. Sellers</A> </I> </ADDRESS> </BODY>