document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165586>Question 1165586</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to Newton’s law of cooling, the temperature of an object changes at a rate proportional to the difference in<BR>\n" );
document.write( "temperature between the object and the outside medium. If an object whose temperature is 70OF is placed in a medium whose<BR>\n" );
document.write( "temperature is 20O and is found to be 40O after 3 minutes, what will its temperature be after 6 minutes?<BR>\n" );
document.write( "a. 25OF b. 28OF c. 31OF d. 34OF </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790149 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=790149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe your answer will be 280.\r<BR>\n" );
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document.write( "the formula i used is f = p * (1 + r) ^ n\r<BR>\n" );
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document.write( "this formula will work off the difference between the temperature of the object and the temperature of the medium.\r<BR>\n" );
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document.write( "in the beginning, the difference is 700 - 200 = 500<BR>\n" );
document.write( "after 3 minutes, the difference is 400 - 200 = 200\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "200 = 500 * (1 + r) ^ 3\r<BR>\n" );
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document.write( "solve for r to get:\r<BR>\n" );
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document.write( "r = (200/500) ^ (1/3) - 1\r<BR>\n" );
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document.write( "that gets you:\r<BR>\n" );
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document.write( "r = -.2631957003.\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "200 = 500 * (1 - .2631957003) ^ 3.\r<BR>\n" );
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document.write( "evaluate the equation to get:\r<BR>\n" );
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document.write( "200 = 200\r<BR>\n" );
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document.write( "this confirms the rate is correct.\r<BR>\n" );
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document.write( "after 6 minutes, the formula becomes:\r<BR>\n" );
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document.write( "f = 500 * (1 - .2631957003) ^ 6.\r<BR>\n" );
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document.write( "solve for f to get:\r<BR>\n" );
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document.write( "f = 80.\r<BR>\n" );
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document.write( "the difference is 80 after 6 minutes.\r<BR>\n" );
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document.write( "since the temperature of the medium is assumed to not change, that means the temperature of the object is 200 + 80 = 280 degrees.\r<BR>\n" );
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document.write( "note that, if the object was placed in the medium forever, then the assumption is that the object will becomes 200 degrees, same as the medium.\r<BR>\n" );
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document.write( "you can graph the function.\r<BR>\n" );
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document.write( "it looks like this.\r<BR>\n" );
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document.write( "to test the claim that eventually it would become 200 degrees, make n a very large number and solve for that.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "f = 500 * (1 - .2631937003) ^ 30 gets you:<BR>\n" );
document.write( "f = .0524288.<BR>\n" );
document.write( "the temperature of the object would then be 200.0524288 degrees.<BR>\n" );
document.write( "that's pretty close to 200.<BR>\n" );
document.write( "make n larger and it will get closer and closer to 200.<BR>\n" );
document.write( "for example, when n = 60, f = .000005<BR>\n" );
document.write( "round to anything less than 5 decimal digits and the difference is 0. </SPAN>\n" );
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