document.write( "Question 1201461: At time t=0, a cup of coffee at 187*d F is placed in a room at 72*d F. After t=4 minutes, the coffee has cooled to a temp of 160*d F. In how many minutes will the coffee reach 130*d F? Round your answer to the nearest 0.01 minutes.\r
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Algebra.Com's Answer #835844 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "At time t=0, a cup of coffee at 187*d F is placed in a room at 72*d F.
\n" ); document.write( "After t=4 minutes, the coffee has cooled to a temp of 160*d F.
\n" ); document.write( "In how many minutes will the coffee reach 130*d F? Round your answer to the nearest 0.01 minutes.
\n" ); document.write( "Any and all help on this problem will be greatly appreciated :)
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document.write( "The Newton law of cooling states that the temperature of the cup of coffee in the room is this function of time t\r\n" );
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document.write( "    T(t) =  = .\r\n" );
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document.write( "where \"k\" is the decay constant.  \r\n" );
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document.write( "At t= 4 minutes  T(t)= 160,  which gives you an equation to find the decay constant k:\r\n" );
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document.write( "    160 = 72 + 115*e^(-k*4),\r\n" );
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document.write( "    115*e^(-k*4) = 160 - 72 = 88,\r\n" );
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document.write( "    e^(-4k) =  = 0.765217.\r\n" );
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document.write( "Take natural logarithms of both sides\r\n" );
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document.write( "    -4k = ln(0.765217)\r\n" );
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document.write( "    k =  = 0.0669.\r\n" );
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document.write( "    +------------------------------------------+\r\n" );
document.write( "    |   Thus the decay constant k is found.    |\r\n" );
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document.write( "The next and last step is to find the time under the question. \r\n" );
document.write( "For it, you have this (the same) Newton's cooling equation \r\n" );
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document.write( "    T(t) =  = 130,\r\n" );
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document.write( "    e(-0.0669*t) =  = 0.50435.\r\n" );
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document.write( "Take natural logarithm of both sides\r\n" );
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document.write( "    -0.0669*t = ln(0.50435)\r\n" );
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document.write( "and find\r\n" );
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document.write( "    t =  = 10.23  minutes  (rounded as requested).  \r\n" );
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document.write( "Answer. 10.23 minutes counting from the very beginning time moment.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "So, the problem is solved in two steps.\r
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\n" ); document.write( "\n" ); document.write( "In the first step, we find the decay coefficient of the cooling equation, using first portion of the given data.\r
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\n" ); document.write( "\n" ); document.write( "In the second step, we find the time getting the given temperature, using the found value of the decay coefficient.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar (and different) solved problems of this type, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Solving problem on Newton Law of cooling \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Learn the subject from there.\r
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