Exponential growth and decay question. (1 Viewer)

[physicss]

The body of a murdered man was discovered at midnight when its temperature was 35*C. One hour later, the temperature of the body had fallen to 34*C. The room temperature was a constant 21*C. Normal body temperature is 37*C. Estimate the time the murder was committed.

Assume equation for temperature is T= S+A(e^-kt) where T is temperature of the body at any time t, and S is the surrounding temperature.

 

[Atrophy]

what's done is done. not here to be number one.

 

[hscishard]

That is one cool question!

 

[random-1006]

The body of a murdered man was discovered at midnight when its temperature was 35*C. One hour later, the temperature of the body had fallen to 34*C. The room temperature was a constant 21*C. Normal body temperature is 37*C. Estimate the time the murder was committed.

Assume equation for temperature is T= S+A(e^-kt) where T is temperature of the body at any time t, and S is the surrounding temperature.

lol, my teacher showed us that question last yr !, cept it was murdered maths teacher lol


we know S=21 ( from question).

take t=0 at midnight

t=0, T=35
t=1, T=34

so 35= 21 +A , A= 14

34= 21 + 14e^-k , solve for k
e^-k= 13/14 --> k= -ln (13/14) or k= ln(14/13), by using log laws, taking the minus sign up and flipping the fraction, thats comes up every now and then on tests.

then you know all the unknowns, set T=37 (ie they had normal body temp just before they died, or we assume they did anyway), solve for t using natural logs, you will get a negative answer, which the amount of hours before midnight, then convert that into hours and minutes and go back from midnight

fairly sure thats it

 

[random-1006]

what's done is done. not here to be number one.

wait a min, was this a trial question??

dont think they would have it as trial question, considering so many people have seen it before

 

[physicss]

thanks random

 

[hscishard]

I somehow equated k and found t is approx -1.074 hrs after midnight.
Do you still have the answer?

 

[physicss]

answer is 10:12pm

 

[hscishard]

Funny. I made an illogical step and still arrived at the answer.