document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129730>Question 1129730</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can someone please assist me in understanding what I am doing wrong:\r<BR>\n" );
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document.write( "A pot of boiling soup with an internal temperature of 100° Fahrenheit was taken off the stove to cool in a 65°F room. After fifteen minutes, the internal temperature of the soup was 95°F. \r<BR>\n" );
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document.write( "Use Newton's Law of Cooling to write a formula <BR>\n" );
document.write( "T(t) that models this situation, where T is the temperature of the soup in degrees Fahrenheit and t is time in minutes. \r<BR>\n" );
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document.write( "Here is my work:<BR>\n" );
document.write( "For the pot of boiling soup;<BR>\n" );
document.write( "A=100-65=35<BR>\n" );
document.write( "T(t)= 35 e^ ( ( kt ) ) +65<BR>\n" );
document.write( "*From there I isolated the variables, took the ln of each equations and then divided the ln of 30/35<BR>\n" );
document.write( "by 15. <BR>\n" );
document.write( "The formula that models the cooling of the soup is<BR>\n" );
document.write( "T(t)= 35 e^( (-0.0103 ) ) +65<BR>\n" );
document.write( "This however keeps being labeled incorrect </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #746321 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=746321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">Here are some thoughts as to why you may have the wrong answer<BR>\n" );
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document.write( "<li>Scenario #1: You forgot to put a lowercase t in the exponent for the term e^( (-0.0103 ) )</li><BR>\n" );
document.write( "<li>Scenario #2: You rounded the decimal value for k in the incorrect format (eg: you rounded to 4 decimal places but maybe your teacher wanted 6 instead)</li><BR>\n" );
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document.write( "Assuming that only scenario #1 applies, then the temperature T(t) function is approximately:<BR>\n" );
document.write( "<font color=red>T(t)= 35*e^(-0.0103*t)+65</font><BR>\n" );
document.write( "You do not need two sets of parenthesis. The asterisk symbols indicate multiplication which may be omitted depending on the computer system your teacher uses.\r<BR>\n" );
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document.write( "As a way to check the answer, let's plug in t = 0 and see what happens\r<BR>\n" );
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document.write( "T(t)= 35*e^(-0.0103*t) + 65<BR>\n" );
document.write( "T(0)= 35*e^(-0.0103*0) + 65 .... replace every lowercase t with 0; use PEMDAS to simplify<BR>\n" );
document.write( "T(0)= 35*e^(0) + 65<BR>\n" );
document.write( "T(0)= 35*1 + 65<BR>\n" );
document.write( "T(0)= 35 + 65<BR>\n" );
document.write( "T(0)= 100\r<BR>\n" );
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document.write( "As expected, we get a result of 100. So when the time is t = 0 minutes (aka the starting point), the temperature is T = 100 degrees Fahrenheit. This is part 1 of confirming the answer.\r<BR>\n" );
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document.write( "Onto part 2: Plug in t = 15. We should get T = 95\r<BR>\n" );
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document.write( "T(t)= 35*e^(-0.0103*t) + 65<BR>\n" );
document.write( "T(15)= 35*e^(-0.0103*15) + 65 ... replace every t with 15<BR>\n" );
document.write( "T(15)= 35*e^(-0.1545) + 65<BR>\n" );
document.write( "T(15)= 35*0.856843492142097 + 65 .... this is approximate<BR>\n" );
document.write( "T(15)= 29.9895222249734 + 65<BR>\n" );
document.write( "T(15)= 94.9895222249734<BR>\n" );
document.write( "If you round to the nearest tenth or the nearest whole number, then you'll get approximately T(15) = 95. Due to rounding error, the 94.9895222249734 should be a lot closer to 95 (or close enough that the calculator can't determine the difference). This concludes showing how after t = 15 minutes, the temperature is now approximately T = 95 degrees F. \r<BR>\n" );
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document.write( "These two parts help verify that the formula <font color=red>T(t)= 35*e^(-0.0103*t)+65</font> is the correct function your teacher wants. Or at least, it's a good approximation of the function.\r<BR>\n" );
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document.write( "Side Note: it's unfortunate that T shows up as the temperature and t is the time, which in my opinion is a bit confusing. It would be more helpful to only use t once. If t is the time, then H could represent the temperature (H for heat maybe) making the function to be H(t)= 35*e^(-0.0103*t) + 65. However, your teacher is using uppercase T for temperature so it's best to stick with that so you don't lose points.</font> </SPAN>\n" );
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