document.write( "Question 929060: Hello, \r
\n" ); document.write( "\n" ); document.write( "I don't know how to solve this problem:\r
\n" ); document.write( "\n" ); document.write( "A cup of coffee which is initially at a temperature of 154 degrees Fahrenheit is placed in a room which is at a constant temperature of 71 degrees. In 10 minutes, the coffee has cooled to 133 degrees. Find the Newton's Law of Cooling formula that models the coffee's temperature in t minutes. Determine to the nearest minute how long it will take the coffee to cool to a temperature of 100 degrees Fahrenheit. \r
\n" ); document.write( "\n" ); document.write( "Thank you in advance,\r
\n" ); document.write( "\n" ); document.write( "Ryan M.
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Algebra.Com's Answer #564285 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!
First off, find Newton's law of cooling,
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\n" ); document.write( "Use the two data points given to find \"k\".
\n" ); document.write( "At \"t=0\",\"T=154\"
\n" ); document.write( "At \"t=10\",\"T=133\",
\n" ); document.write( "\"k%280-10%29=-ln%28%28154-71%29%2F%28133-71%29%29\"
\n" ); document.write( "\"-10k=-0.291716\"
\n" ); document.write( "\"k=0.02917\"
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\n" ); document.write( "So now find \"t\" when \"T=100\",
\n" ); document.write( "Then,
\n" ); document.write( "\"0.02917%280-t%29=-ln%28%28154-71%29%2F%28100-71%29%29\"
\n" ); document.write( "\"-0.02917t=-1.0515\"
\n" ); document.write( "\"t=36.05\"\"minutes\"
\n" ); document.write( "To the nearest minute,
\n" ); document.write( "\"t=36\"
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