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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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.