A body was found at 6 a.m. outdoors on a day when the temperature was 50oF. The medical examiner found the temperature of the body to be 66oF. What was the approximate time of death? Use Newton's law of cooling, with k = 0.1947.

A. Midnight (12 a.m.)

B. 5 a.m.

C. 2 a.m.

D. 3 a.m.

Midnight actually. Just took the test

T(t) = To + (50-To)e^-.1947t

I think we can assume that To = 98.6, so

T(t) = 98.6 - 48.6 e^-.1947t

So, just solve for t in T(t) = 66.

That will give the number of hours since death (t=0).

okay thanks :)

To determine the approximate time of death, we can apply Newton's law of cooling. This law states that the rate at which an object changes temperature is directly proportional to the difference between its temperature and the temperature of its surroundings.

The formula for Newton's law of cooling is:
dT/dt = -k(T - Ts)

Where:
dT/dt is the rate of change of temperature,
k is the cooling constant,
T is the temperature of the body at time t, and
Ts is the temperature of the surroundings.

In this case, we know the following values:
Initial temperature of the body, T0 = 66°F
Temperature of the surroundings, Ts = 50°F
Cooling constant, k = 0.1947

We can rearrange the formula to solve for time, t:
dT/dt = -k(T - Ts)
dt/dT = -1/k(T - Ts)
∫dt = -1/k ∫(T - Ts) dT
t = -1/k * ln(T - Ts) + C

Since we are looking for the time of death, we can set C = 0.

Now, substituting the known values into the equation, we get:
t = -1/0.1947 * ln(66 - 50)
t ≈ -1/0.1947 * ln(16)
t ≈ -1/0.1947 * 2.77259
t ≈ -14.2359

Since negative time values are not meaningful in this context, we can discard the negative sign and approximate the time of death as approximately 14.2359 hours before the body was found.

Given that the body was found at 6 a.m., we can subtract 14.2359 hours from that time to approximate the time of death.

6 a.m. - 14.2359 hours ≈ 3.7641 a.m.

Therefore, the approximate time of death is approximately 3 a.m. (Option D).

2 am