Respuesta :
Answer:
Time of murder = 10:39 am
Step-by-step explanation:
Let the equation of exponential function representing the final temperature of the body after time 't' is,
f(t) = [tex]a(e)^{nt}[/tex]
Here, a = Initial temperature
n = Constant for the change in temperature
t = Duration
At 11:30 am temperature of the body was 91.8°F.
91.8 = [tex]98.6(e)^{nt}[/tex] --------(1)
Time to reach the body to the morgue = 12:30 pm
Duration to reach = 12:30 p.m. - 11:30 a.m.
= 1 hour
Therefore, equation will be,
84.4 = [tex]91.8(e)^{n\times 1}[/tex]
eⁿ = [tex]\frac{84.4}{91.8}[/tex]
ln(eⁿ) = ln(0.9194)
n = -0.08403
From equation (1),
91.8 = [tex]98.6(e)^{-0.08403t}[/tex]
[tex](e)^{0.08403t}=\frac{98.6}{91.8}[/tex]
[tex]ln[(e)^{0.08403t}]=ln[\frac{98.6}{91.8}][/tex]
0.08403t = 0.07146
t = 0.85 hours
t ≈ 51 minutes
Therefore, murder was done 51 minutes before the detectives arrival.
Time of murder = 11:30 - 00:51
= 10:90 - 00:51
= 10:39 am
