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Help with math problem (exponential decay, differential equations)
    #14726228 -

Here is the problem:

Suppose that a corpse is discovered at 10 p.m. and its temperature is determined to
be 85o F. Two hours later, its temperature is 74o F. If the ambient temperature is
68o F, estimate the time of death.

The "o F" just stands for degrees Fahrenheit...

Can anyone help?  If so, please show your work, if someone can just get me started I should be able to solve it.

Thanks


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Re: Help with math problem (exponential decay, differential equations) [Re: Celestial Traveler]
    #14726268 -

well i havnt done partial differential equations, but i know with exponential decay you can use logarithmic equations (base e or natural log).

i think you might be able to use a modified version of the generic formula Ce^-kt and find the coefficient k with t=0 at 10pm and c=85 degrees?

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Re: Help with math problem (exponential decay, differential equations) [Re: grimrs]
    #14726320 -

grimrs said:
well i havnt done partial differential equations, but i know with exponential decay you can use logarithmic equations (base e or natural log).

i think you might be able to use a modified version of the generic formula Ce^-kt and find the coefficient k with t=0 at 10pm and c=85 degrees?


That's the thing, the time of death is at t = 0 so therefore 10 pm is NOT t = 0...also this is an ordinary differential equation problem, not a partial one.


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Re: Help with math problem (exponential decay, differential equations) [Re: Celestial Traveler]
    #14726340 -

My first thought is "Newton's law of cooling" where the change in temperature is linearly proportional to the difference from ambient temperature.  The difference in ambient temperature is a function of time, just like the change in body temperature.

Formula: 0

Does that look reasonable to you?  I think thats a good place to start.

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Re: Help with math problem (exponential decay, differential equations) [Re: DieCommie]
    #14726351 -

Yeah I get what you're saying...you're using differentials but differentials are an estimate, not a precise calculation.


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Re: Help with math problem (exponential decay, differential equations) [Re: Celestial Traveler]
    #14726394 -

Don't confuse the derivative on the left with the delta on teh right.  The derivative on the left is the instantaneous rate of temperature change.  The delta on the right is the finite temperature difference between the surroundings and the body, something like this Formula: 0.  Each of these temperatures could be done as linear expressions with respect to the time.  Then think about what the differential equation looks like and what kind of solutions it may have.  (Hint:  Look at your thread title)

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Re: Help with math problem (exponential decay, differential equations) [Re: DieCommie]
    #14726439 -

DieCommie said:
Don't confuse the derivative on the left with the delta on teh right.  The derivative on the left is the instantaneous rate of temperature change.  The delta on the right is the finite temperature difference between the surroundings and the body, something like this Formula: 0.  Each of these temperatures could be done as linear expressions with respect to the time.  Then think about what the differential equation looks like and what kind of solutions it may have.  (Hint:  Look at your thread title)


Ah I see...it looked like the T on the right was the same function as the one being differentiated on the left...but thanks.


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Re: Help with math problem (exponential decay, differential equations) [Re: Celestial Traveler]
    #14726449 -

Yea, Im a little sloppy due to laziness.  The T on the left in the differential would be T_B.

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Re: Help with math problem (exponential decay, differential equations) [Re: DieCommie]
    #14726474 -

Word it's all good.


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