LOG PROJECT: MURDER MYSTERY
You’ve all been shipwrecked on a tropical island - a wonderful place, with bananas, coconuts, fish, and a pretty
constant temperature of 80°. Your teacher, Mr. Roemer, has been murdered. You know there’s no one else on
the island - it was one of your classmates that did it! None of you will sleep peacefully in your flimsy grass huts
until the murderer is discovered.
You have watches, thermometers, and other simple tools, but no experts on murder investigations. The day
Mr. Roemer was murdered, everyone was walking around the island by two’s, noting its features, in hopes
that would help you all figure out where you are. It turns out that everyone walked by the spot where Mr.
Roemer’s body was found, and recorded the time when they were at a nearby spot (where they could see a
volcano on the next island). Figuring out the time of death would likely narrow down the suspects to four or
less.
Nic had a hunch that knowing the body temperature would help determine the time of death. So, at 1 pm, he
checked the temperature of Mr. Roemer’s corpse. It was 96.1°. Then at 2 pm, it was 91.7°.
Finding the murderer will be our goal. It might take us a few days. (I hope you don’t mind some sleepless
nights...)
One more clue… this comes from Mrs. Boling, “I read a lot of murder mysteries. In one of them, this detective
says, ‘A dead body cools off just like a hot cup of joe.’ I don’t know if that helps or not…”
You’ll also need to know:
� = � + � ∗ ��
Where: B: is the body temp (usually 98.6°)
A: is the temperature of the air
E: is how much hotter the body was than the air when first measured.
b: is the ratio of the temperature
t: is the time measured in hours.
Extra Credit Due Date: 05/11/2015
20 40 60
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80
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160
x
y
PART 1
We want to think about how a hot cup of coffee cools off.
1. What would be a reasonable starting temperature?
2. After about how long would it be cold?
3. About what temperature is it when it’s cold? (Why?)
4. Now let time be the x-axis (t-axis) and temperature (T)
be the y-axis, and graph temperature versus time for a
cup of coffee, using what you know from common sense.
Does a straight line graph make sense for this?
PART 2
Sara says “We need some numbers here.” And she boils some coffee up over a campfire and measures its
temperature with a thermometer Dylan provides.
Here’s what she gets:
The coffee starts out at 176 degrees,
and cools off like this…
Min Degrees
1 169
2 162
3 156
5 146
10 125
15 111
20 101
30 90
60 81
5. If he measured the coffee at 2 hours and 3 hours, what temperature would it be?
6. Graph this data, and connect the points with a smooth curve.
7. So we can conclude that this graph has what line as an asymptote?
8. Give an example of a function with this asymptote.
x
y
PART 3
Mr. Roemer’s dead body was lying near the viewing spot for the volcano, and it turns out that there was only
one path going by that spot. So, after checking with each other, and remembering who passed whom, you all
agree that the murderer was most likely one of the people at that spot right before or after the time of death.
Below are the times that each pair walked by the volcano viewing spot:
When you figure out the time of
death, you’ll know the 4 most likely
suspects.
9. B: ______
10. A: ______
11. Initial body temp: ______
12. E: (How much hotter was the initial body temp than the air temp?):
______
13. b (Ratio of current temperature over initial temperature taken): ____
14. Write the function: (� = � + � ∗ ��): __________________
15. Rewrite the exponential function as a log:
16. Solve for t:
17. Time of Death (absolute value of t hours BEFORE initial time):
18. Suspects:
Sara and Ana 9:05
Baylee and Nic 9:20
James and Carlos 9:35
Dylan and Natalie 9:50
Kaleb and Cynthia 10:05
Jacob and Robert 10:20
Seth and Markus 10:35
Leah and Logan 10:40
Joshua and Jamison 10:55
PART 4: THE NEXT DAY
Of course, all 4 suspects swear they’re innocent. The next day, Baylee finds Mrs. Boling dead, left lying right in
the clearing.
My body temperature is 93.1°, and it’s 9:46pm. You check at 10:16pm, and it’s 87.2°.
Here’s everyone’s alibis:
• James, Jamison, Seth, and Joshua were all swimming together from 8am to 9:30am.
• Sara, Natalie, Dylan, Ana, and Carlos were all looking for clams together from 8:30am
to 9:30am.
• Robert, Jacob, Nick, and Baylee were all gathering coconuts together from 9am until
they heard Mrs. Boling’s screams.
• Kaleb, Logan, Leah, Cynthia, and Markus were hiking from 9:30 until they heard the
screams.
Please find the killer before someone else is murdered!
19. B: ______
20. A: ______
21. Initial body temp: ______
22. E: (How much hotter was the initial body temp than the air temp?): ______
23. Time between temperatures taken (in hours):_______
24. b (Ratio of current temperature over initial temperature, and then raised to the power of the time
between temperatures): ______
25. Write the function: (� = � + � ∗ �� ): __________________
26. Rewrite the exponential function as a log:
27. Solve for t:
28. Time of Death (absolute value of t hours BEFORE initial time):
29. Suspects:
30. Now you’re the prosecuting attorney, and you need to write up a closing argument explaining to the
jury how we know the time of death, and why that means the prime suspect is the killer.