Results 1 to 5 of 5

Math Help - how many hours elapsed when the body was found...

  1. #1
    Senior Member
    Joined
    Aug 2009
    Posts
    349

    how many hours elapsed when the body was found...

    a dead body was found within a closed room of a house where the temperature was a constant 70 F. at the time of discovery the core temperature of the body was determined to be 85 F. one hour later a second measurement showed that the core temperature of the body was 80 F. assume that the time of death corresponds to t=0 and that the core temp at that time was 98.6 F, how many hours elapsed before the body was found?


    ok so my equation that i want to use will be T = Tm + Ce^(kt)
    so can i say that t(0)= 98.6 F. if that is true then i can find my C value and have the actual problem set up. but im not sure where to go after this. I know i need to find k and then eventually t...which my book says is 1.6 hours

    well any help would be appreciated..thanks in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi
    The temperature of the body is T(t) = T_m + Ce^{kt}, k being negative
    We know that :
    - at infinite time T(t) is the temperature of the room, therefore Tm=70
    - T(0)=98.6=Tm+C therefore we know the value of C

    The temperature of the body at the time it was found is T_1 = T_m + Ce^{kt} = 85
    One hour later T_2 = T_m + Ce^{k(t+1)} = 80

    Now you just have to solve
    Follow Math Help Forum on Facebook and Google+

  3. #3
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    Don't confuse capital T with lowercase t in Newton's Law of Cooling problems! Highly dangerous. Might get a negative citation from the Citation Writing Subgroup of the Committee for the Prevention of Notational Abuse.

    I would agree that T(0) = 98.6.

    The target variable is the time at which the temperature is 85 degrees, call it t_{d}, for the time of discovery. You know that

    T(t_{d})=85, and you also know that

    T(t_{d}+1)=80.

    With your underlying equation of

    T=70+Ce^{kt},

    you should be able to find what you're looking for. Make sense?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Aug 2009
    Posts
    349
    yeah that does make sense, that was the trick that i missed! that was the missing link the Td and then Td+1....

    thanks!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    You're welcome!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How was this result found
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: January 3rd 2011, 07:56 AM
  2. [SOLVED] Almost found limit of sum
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 30th 2010, 06:21 AM
  3. Just found this website
    Posted in the Math Forum
    Replies: 0
    Last Post: July 1st 2010, 08:19 AM
  4. [SOLVED] Time elapsed (SHM)?
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: June 3rd 2009, 01:53 PM

Search Tags


/mathhelpforum @mathhelpforum