document.write( "Question 1130119: Could someone please assist with the question:
\n" ); document.write( "A pot of boiling soup with an internal temperature of 100� Fahrenheit was taken off the stove to cool in a 69�F room. After fifteen minutes, the internal temperature of the soup was 93�F. \r
\n" ); document.write( "\n" ); document.write( "To the nearest minute, how long will it take the soup to cool to 81�F? \r
\n" ); document.write( "\n" ); document.write( "Here is my work:
\n" ); document.write( "69+(100-69) * e= 69+31*e
\n" ); document.write( "93=69+31*e(-k*15)
\n" ); document.write( "31*e^(-k *15)= 93-69= 24
\n" ); document.write( "e^-15k= 24/31= .7742
\n" ); document.write( "-15K= ln(.7742)
\n" ); document.write( "k= -ln(0.7742)/ 15=0.017\r
\n" ); document.write( "\n" ); document.write( "T(t)= 69+31*e (0.017)=81
\n" ); document.write( "e(-0.017*t)= 81-69/31=.387
\n" ); document.write( "-0.017*t= ln(.387)
\n" ); document.write( "t= - ln (.387)/ (0.017)= 55.8 min
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Algebra.Com's Answer #853973 by MathTherapy(10801)\"\" \"About 
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document.write( "Could someone please assist with the question: \r\n" );
document.write( "A pot of boiling soup with an internal temperature of 100� Fahrenheit was taken off the stove to cool in a 69�F room.\r\n" );
document.write( "After fifteen minutes, the internal temperature of the soup was 93�F. \r\n" );
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document.write( "To the nearest minute, how long will it take the soup to cool to 81�F? \r\n" );
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document.write( "Here is my work:\r\n" );
document.write( "69+(100-69) * e= 69+31*e\r\n" );
document.write( "93=69+31*e(-k*15)\r\n" );
document.write( "31*e^(-k *15)= 93-69= 24\r\n" );
document.write( "e^-15k= 24/31= .7742\r\n" );
document.write( "-15K= ln(.7742)\r\n" );
document.write( "k= -ln(0.7742)/ 15=0.017\r\n" );
document.write( "\r\n" );
document.write( "T(t)=  69+31*e (0.017)=81\r\n" );
document.write( "e(-0.017*t)= 81-69/31=.387\r\n" );
document.write( "-0.017*t= ln(.387)\r\n" );
document.write( "t= - ln (.387)/ (0.017)= 55.8 min\r\n" );
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document.write( "You can use Newton's Law of Cooling.......any of the following 3 formulae should work: \r\n" );
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document.write( "This author's preference is the 1st formula. In this case, the cooling rate is first needed, and is derived as follows:\r\n" );
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document.write( "       , where: \"t\" = time taken to get to a COOLED temperature (15 minutes, in this case)\r\n" );
document.write( "                                             \"T%28t%29\" = TEMPERATURE (T) at a given time (t)___(93oF, in this case) \r\n" );
document.write( "                                              \"T%5Bs%5D\" = SURROUNDING Temperature (69oF, in this case)\r\n" );
document.write( "                                              \"T%5Bo%5D\" = ORIGINAL/INITIAL temperature (100oF, in this case)\r\n" );
document.write( "                                               \"k\" = the CONSTANT or COOLING rate (UNKNOWN, in this case)\r\n" );
document.write( "                                      \r\n" );
document.write( "                                       ----- Substituting 15 for t, 69o for \"T%5Bs%5D\", and 100o for \"T%5Bo%5D\"\r\n" );
document.write( "                                             \"matrix%281%2C3%2C+93%2C+%22=%22%2C+69+%2B+%28100+-+69%29+%2A+e%5E%28-+15k%29%29\" ----- Substituting 93o for T(15)\r\n" );
document.write( "                                             \r\n" );
document.write( "                                       \"matrix%281%2C3%2C+-+15k%2C+%22=%22%2C+ln+%2824%2F31%29%29\" ----- Converting to NATURAL LOGARITHMIC (ln) form\r\n" );
document.write( "                                              \"matrix%281%2C5%2C+k%2C+%22=%22%2C+ln%2824%2F31%29%2F%28-+15%29%2C+%22=%22%2C+0.0170622%29\"\r\n" );
document.write( "***********************************************************************\r\n" );
document.write( "To the nearest minute, how long will it take the soup to cool to 81�F?\r\n" );
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document.write( "                                    \r\n" );
document.write( "                                       ----- Substituting 69o for \"T%5Bs%5D\", 100o for \"T%5Bo%5D\", and .0170622 for k\r\n" );
document.write( "                                          \"matrix%281%2C3%2C+81%2C+%22=%22%2C+69+%2B+%28100+-+69%29+%2A+e%5E%28-+.0170622t%29%29\" ----- Substituting 81o for T(t)\r\n" );
document.write( "                                          \r\n" );
document.write( "                        \"matrix%281%2C3%2C+-+.0170622t%2C+%22=%22%2C+ln+%2812%2F31%29%29\" ----- Converting to NATURAL LOGARITHMIC (ln) form\r\n" );
document.write( "Time it takes for the soup to cool to 81oF, or \r\n" );
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document.write( "As your answer, 55.8 min, or approximately 56 mins, coincides with mine, it is correct!\r\n" );
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document.write( "Great JOB!!
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