Question

When was the Murder Committed? The police discover the body of a murder victim. Critical to solving the crime is determining when the murder was committed. The coroner arrives at the murder scene at 12:00 P.M. She immediately takes the temperature of the body and finds it to be 94.6F. She then takes the temperature 1 hr later and finds it to be 93.4F. The temperature of the room is 70F. When was the murder committed? (Assume that the normal human body temperature is 98.6 F)

Answer 1

Have you studied Newton's Law of Cooling yet?

Answer 2

all you have to do is plug into the equation
u(t)=z+(u0-z)e^-kt

solve for k

Answer 3

once you find k you plug back into equation and solve for t

Answer 4

\[u(t)=\sigma+(U _{0}-\sigma)e ^{-kt}\]

Answer 5

sigma is the room temp
U_0 is the temp at which the body was found
t is the time in hours later
u(t) is the temp after the time

plug in and solve for k

Answer 6

so that would be 93.4= 70+(94.6-70)e^K(1) something like that?

Answer 7

that is exactly right... now once you solve for k, you have to plug back into the original equation except instead of using 93.4 you will use 98.6 and solve for t, that that will tell you how many hours it was before 12 when the body was found

Answer 8

i mean how many hours before 12 when the person died.

Answer 9

93.4= 70+(94.6-70)e^-K(1) for k then 98.6=70+(94.6-70)e^k(1) or?

Answer 10

I ♥ murders!!!

Answer 11

I got k= -0.1282

Answer 12

the first one is right, and the second one is right except that whatever k value you got from the first equation you plug into the second, and solve for t instead, since you are trying to find time

Answer 13

98.6=70+(94.6-70)e^-0.1282(t) ?

Answer 14

t= 1.3216

Answer 15

solving for k for the first equation
ln(23.4/24.6)/-1= k

i dont have a calculator to check is that what you got

Answer 16

I got k= -0.1282

Answer 17

i think k should be positive, let me find a calculator