Final answer:
To determine the time of death, we assume a linear decrease in body temperature over time. We convert the Celsius temperature to Fahrenheit and calculate the temperature at the time of death. Using the measured temperatures and a linear regression model, we find the equation of the line representing the decrease in temperature. Substituting the temperature at the time of death into the equation gives us the time of death.
Step-by-step explanation:
To determine the time of death, we will assume that the body temperature decreases linearly over time. We will use a linear regression model to find the equation of the line that represents the decrease in temperature from the measured values. Let's denote the temperature at 2 PM as T1, the temperature at 3 PM as T2, and the temperature at the time of death as Td. We have the following data:
Time (in hours): 2, 3
Temperature (in °F): 94.1, 92.7
First, we need to convert the Celsius temperature to Fahrenheit. The average normal body temperature is given as 37.0 °C (98.6 °F). Using this, we can calculate the temperature at the time of death in Fahrenheit:
Td = 98.6 * (9/5) + 32 = 209.48 °F
Next, we can use the formula for the equation of a line to find the equation that represents the decrease in temperature:
T = mx + c
where T is the temperature, x is the time in hours, m is the slope, and c is the y-intercept.
Using the values T1 = 94.1, T2 = 92.7, x1 = 2, x2 = 3, we can find the values of m and c:
m = (T2 - T1) / (x2 - x1) = (92.7 - 94.1) / (3 - 2) = -1.4 °F/hr
c = T1 - m * x1 = 94.1 - (-1.4 * 2) = 96.9 °F
Now that we have the equation of the line, we can substitute Td into the equation and solve for x to find the time of death:
Td = -1.4x + 96.9
209.48 = -1.4x + 96.9
-1.4x = 209.48 - 96.9
-1.4x = 112.58
x = 112.58 / -1.4
x ≈ -80.415
Since time cannot be negative, we will take the absolute value of x, which gives us approximately 80.415. This means the murder occurred 80 hours and 25 minutes before 2 PM.