Question

This exercise uses Newton's Law of Cooling.

Newton's Law of Cooling is used in homicide investigations to
determine the time of death. The normal body temperature is 98.6°F.
Immediately following death, the body begins to cool. It has been
determined experimentally that the constant in Newton's Law of
Cooling is approximately *k* = 0.1947, assuming time is
measured in hours. Suppose that the temperature of the surroundings
is 55°F.

(a) Find a function *T*(*t*) that models the
temperature *t* hours after death.

T(t) = |

(b) If the temperature of the body is now 73°F, how long ago was
the time of death? (Round your answer to the nearest whole
number.)

hr

Answer #1

Use Newton's law of cooling model to partially solve a murder
mystery. At 3:00 p.m. a deceased body is found. Its temperature is
70+ F. An hour later the body temperature has decreased to 60+ .
It's been a winter inversion in SLC, with constant ambient
temperature 30+ . Assuming the Newton's law model, estimate the
time of death

Newton's law of cooling states that the temperature of an object
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Newton's Law of Cooling tells us that the rate of change of the
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TT is the temperature of the object after tt units of time have
passed, AA is the ambient temperature of the object's surroundings,
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Suppose that a cup of coffee begins at 179179 degrees and,...

(1 point) Newton's Law of Cooling states that the rate of
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the temperature of the object, and Ts is the surrounding
temperature. The following differential equation describes Newton's
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. Assume that the interior temperature is Ti = 77F, when the
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Question B:
Newton's law of cooling states
dθ/dt = −k (θ−T)
where ? is the temperature at time t, T is the constant
surrounding temperature and k is a constant.
If a mass with initial temperature, θ0, of 319.5 K is
placed in a surroundings of 330.5 K, and k is 0.011 s-1
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____________

Cooling:
The body of an apparent victim of a crime is discovered
by detectives at 9 AM, at which time the body temperature was
measured to be 88°. Two hours later the temperature was 82°. Using
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A body was found in the basement of the Underwater Basket
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steady 65 degrees Fahrenheit. When found, the core temperature was
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temperature had fallen to 88.4. Assuming that the body
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1. Graph this function in an appropriate window and sketch
below. (Please write and show the graph)
2. What happens to this function as time goes by? Why does this
make sense?
3. Use the graph...

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