document.write( "Question 1188251: A pan of water is brought to a boil and then removed from the heat. Every 5 minutes thereafter the difference between the termperature of the water and room temperature is reduced by 50%. \r
\n" ); document.write( "\n" ); document.write( "a) Room temperature is 20 degrees Celcius. Express the temperature of the water as a function of the time since it was removed from the heat. \r
\n" ); document.write( "\n" ); document.write( "b) How many minutes does it take for the termperature of the water to reach 30 degree Celcius. \n" ); document.write( "

Algebra.Com's Answer #819302 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "A pan of water is brought to a boil and then removed from the heat.
\n" ); document.write( "Every 5 minutes thereafter the difference between the temperature
\n" ); document.write( "of the water and room temperature is reduced by 50%.
\n" ); document.write( "a) Room temperature is 20 degrees Celsius. Express the temperature of the water
\n" ); document.write( "as a function of the time since it was removed from the heat.
\n" ); document.write( "b) How many minutes does it take for the temperature of the water to reach 30 degree Celsius.
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\n" ); document.write( "\n" ); document.write( "            It is a STANDARD problem on the Newton's law of cooling,\r
\n" ); document.write( "\n" ); document.write( "            which is a standard application of logarithms and exponential functions.\r
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\n" ); document.write( "\n" ); document.write( "            So, it is TOTALLY GOOD ( legal ) for this forum.\r
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document.write( "I will assume that the boiling temperature is 100 °C (standard for water at normal conditions).\r\n" );
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document.write( "Then according to the Newton's cooling law, the temperature of the water at any time moment t \r\n" );
document.write( "after removing from the heat is\r\n" );
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document.write( "    T(t) = 20 + .\r\n" );
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document.write( "This formula is the answer to your first question (a).\r\n" );
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document.write( "To answer your second question, write this equation as you read the problem\r\n" );
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document.write( "    30 = .\r\n" );
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document.write( "Simplify it step by step\r\n" );
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document.write( "    30 - 10 = \r\n" );
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document.write( "      20    = \r\n" );
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document.write( "       = \r\n" );
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document.write( "       = .\r\n" );
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document.write( "At this point, the answer is OBVIOUS:   = 2,  or  t = 2*5 = 10 minutes.\r\n" );
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document.write( "It is the answer to your second question (b).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved and thoroughly explained in all details.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar (and different) cooling problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Solving problem on Newton Law of cooling \r
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