A corpse was discovered in a motel room at midnight and uts temperature was 82°F. The temperature dropped to 80.5°F two hours later. Given k is a constant for the object in question, S is the surrounding temperature, t represents the time and theta(of time) is the temperature at the given time, Newton's Law of Cooling states:
K(t1-t2)=-ln((theta)(t1)-S)/((theta)(t2)-S)
Find the time of death to the nearest minute
Find a function that graphs hours since death as a function of body temperature.
Thanks ahead of time!
Are you confusing k and θ?
I see no k in the function.
It also appears you are missing some information. Ought we not to know S?
To find the time of death, we can use Newton's Law of Cooling formula. Let's label the time of death as t1 and the time when the temperature dropped to 80.5°F as t2.
The formula can be written as:
K(t1 - t2) = -ln((θ(t1) - S) / (θ(t2) - S))
We know that the temperature at the time of death (t1) was 82°F, and two hours later (t2), it dropped to 80.5°F. Additionally, we need to know the surrounding temperature (S) to calculate the constant (K). However, the surrounding temperature is not given in the question. Without the value for S, we cannot proceed to find the exact time of death.
To graph hours since death as a function of body temperature, we need to determine the value of the constant K. Again, since S is not provided, we cannot calculate the exact value of K for this specific scenario. However, I can provide you with a general function that would graph hours since death as a function of body temperature using K as a constant.
Let's assume we have the constant K and the surrounding temperature S. We can manipulate the Newton's Law of Cooling formula to solve for t1:
K(t1 - t2) = -ln((θ(t1) - S) / (θ(t2) - S))
Rearranging the equation, we get:
t1 = (ln((θ(t1) - S) / (θ(t2) - S))) / K + t2
The function that graphs hours since death (t1 - t2) as a function of body temperature (θ(t1)) would be:
f(θ(t1)) = ((ln((θ(t1) - S) / (θ(t2) - S))) / K) + t2
Please note that without the specific values for the constants K and S, it is not possible to provide an exact solution.