document.write( "Question 1126746: A cup of coffee has cooled from 92degreesC to 50degreesC after 13 minutes in a room at 24degreesC. How long will it take to cool to 30degreesC?\r
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Algebra.Com's Answer #743077 by ikleyn(52832) $\"\"$ $\"About$

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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= 13 minutes  T(t)= 50,  which gives you an equation to find the decay constant k:\r\n" );
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document.write( "    50 = 24 + 68*e^(-k*13)\r\n" );
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document.write( "    68*e^(-k*13) = 50 - 24 = 26\r\n" );
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document.write( "    e^(-13k) =  = 0.3823\r\n" );
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document.write( "    - 13k = ln(0.3823)\r\n" );
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document.write( "    k =  = 0.074.\r\n" );
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document.write( "Thus the decay constant k is found.\r\n" );
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document.write( "The last step is to find the time under the question. For it, you have this equation\r\n" );
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document.write( "    T(t) =  = 30\r\n" );
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document.write( "    e(-0.074*t) =  = 0.088\r\n" );
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document.write( "    -0.074*t = ln(0.088)\r\n" );
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document.write( "    t =  = 32.8\r\n" );
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document.write( "Answer. 32.8 minutes counting from the very beginning time moment.\r\n" );
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