SOLUTION: A coroner found that the temperature of a murdered body was 90 F at 11:00 pm and 88.5 F an hour later. The temperature of the room was 70 F. According to Newton�s law of Cooling,

Question 1116711: A coroner found that the temperature of a murdered body was
90 F at 11:00 pm and 88.5 F
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
c and k are constants. Normal body temperature is
98.6 F. Find the values of c and k .
Determine when the murder was committed.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
98.6=70+c*e^0
c=28.6 ANSWER
90=70+28.6*e^kt
88.5=70+28.6e^k(t+1)
From the first:
0.6993=e^kt
ln both sides
kt=-0.3577
From the second:
18.5=28.6*(e^kt)*e^k
0.6469=e^k(t+1)
ln both sides
-0.4356=k(t+1)=kt + k
-0.4356+0.3577=-0.0779=k, by substitution ANSWER
kt=-0.3577
-0.0779*t=-0.3577
t=4.59 hours earlier than 11 pm or 6.41 hours time or 6:25 pm to the nearest minute ANSWER
check
t(4.59)=70+28.6*e*(4.59*(-0.0779)
=70+20=90
at 5.59 hours
t(5.59=70+28.6(e^(5.59*(-0.0779))=88.5

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