document.write( "Question 1116711: A coroner found that the temperature of a murdered body was
\n" ); document.write( "90 F at 11:00 pm and 88.5 F
\n" ); document.write( "an hour later. The temperature of the room was 70 F. According to Newton’s law of Cooling, the temperature, in F, of the body at time T, in hours, is given by T(t)=70+ce^kt, where
\n" ); document.write( "c and k are constants. Normal body temperature is
\n" ); document.write( "98.6 F. Find the values of c and k .
\n" ); document.write( "Determine when the murder was committed. \n" ); document.write( "
Algebra.Com's Answer #732050 by Boreal(15235)\"\" \"About 
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98.6=70+c*e^0
\n" ); document.write( "c=28.6 ANSWER
\n" ); document.write( "90=70+28.6*e^kt
\n" ); document.write( "88.5=70+28.6e^k(t+1)
\n" ); document.write( "From the first:
\n" ); document.write( "0.6993=e^kt
\n" ); document.write( "ln both sides
\n" ); document.write( "kt=-0.3577
\n" ); document.write( "From the second:
\n" ); document.write( "18.5=28.6*(e^kt)*e^k
\n" ); document.write( "0.6469=e^k(t+1)
\n" ); document.write( "ln both sides
\n" ); document.write( "-0.4356=k(t+1)=kt + k
\n" ); document.write( "-0.4356+0.3577=-0.0779=k, by substitution ANSWER
\n" ); document.write( "kt=-0.3577
\n" ); document.write( "-0.0779*t=-0.3577
\n" ); document.write( "t=4.59 hours earlier than 11 pm or 6.41 hours time or 6:25 pm to the nearest minute ANSWER
\n" ); document.write( "check
\n" ); document.write( "t(4.59)=70+28.6*e*(4.59*(-0.0779)
\n" ); document.write( "=70+20=90
\n" ); document.write( "at 5.59 hours
\n" ); document.write( "t(5.59=70+28.6(e^(5.59*(-0.0779))=88.5\r
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