At 1:00 a.m, a homocide detective found the reading of a corpse's body temperature to be 88 degrees Fahrenheit . One hour later, the body temperature is 83 degrees Fahrenheit. If the body has been in a 74 degrees Fahrenheit room since its death, what is the time of death assuming the body was at 98.6 degrees Fahrenheit at its death!
My answer: the equation is y=196/9(9/14)^x+74
When y=98.6
X is equal to -0.3
Is it -0.3 hour??
-0.3*60... How do you figure out the time?
I assume x is the number of hours since death (but y(0) = 95.7, which does not agree with the requirement that y(0) = 98.6)
Anyway, if you want to find the value of x for a given body temperature y using your equation,
y = 196/9 (9/14)^x + 74
(9/14)^x = 9/196 (y-74)
x = ln(9/196 (y-74))/ln(9/14)
= -0.4418 (ln(9/196) + ln(y-74))
= 1.3612 - 0.4418ln(y-74)
Fix the equation as needed and solve for x as above.
To find the time of death, we can use the concept of post-mortem cooling or the Newton's Law of Cooling. This law states that the rate of change of temperature of an object is proportional to the difference between its current temperature and the temperature of its surroundings.
In this case, we know that the initial body temperature (at the time of death) was 98.6 degrees Fahrenheit and the body was found with a temperature of 88 degrees Fahrenheit at 1:00 a.m. We also know that one hour later, at 2:00 a.m., the body temperature had dropped to 83 degrees Fahrenheit.
Let's assume the time of death is 't' hours before the body was found at 1:00 a.m. We can set up an equation using the information given:
Body temperature at 1:00 a.m. = Temperature of the surroundings + (Body temperature at time of death - Temperature of the surroundings) * e^(-kt)
Here, 'e' is the mathematical constant approximately equal to 2.71828, 'k' is the proportionality constant, and the exponential term e^(-kt) represents the decay or cooling of the body over time.
Using the given information, the equation can be rewritten as:
88 = 74 + (98.6 - 74) * e^(-k)
Similarly, for the temperature at 2:00 a.m.:
83 = 74 + (98.6 - 74) * e^(-k)
We now have a system of two equations with two unknowns (k and t). Solving these equations simultaneously will give us the values of k and t, which will help us determine the time of death.
Using the provided equation y = (196/9) * (9/14)^x + 74 seems to be an approach that assumes exponential decay and uses logarithms to solve for the value of x. However, the derivation and validity of this equation are not clear in this context. Thus, to accurately determine the time of death, it's recommended to use the Newton's Law of Cooling or post-mortem cooling method described above.