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serenabrown34
23.03.2021 •
Mathematics
The Law and Order detectives enter a house at 11:30 am and found a man on the floor murdered. They take his body temperature finding to be 91.8 F. The body is taken to the morgue and at 12:30 pm the body temperature is 84.4 F. Using an exponential model for the body temperature, to the nearest minute, what time was he killed. Normal body temperature is 98.6.
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Ответ:
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) =![a(e)^{nt}](/tpl/images/1214/4385/d4d39.png)
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 =
--------(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 =![91.8(e)^{n\times 1}](/tpl/images/1214/4385/c0171.png)
eⁿ =![\frac{84.4}{91.8}](/tpl/images/1214/4385/c108b.png)
ln(eⁿ) = ln(0.9194)
n = -0.08403
From equation (1),
91.8 =![98.6(e)^{-0.08403t}](/tpl/images/1214/4385/8a80a.png)
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
Ответ:
b
Step-by-step explanation: