You and other members of Math Iz Us were camping on the grounds of a large country estate in Britain, when you were roused from sleep by unusual sounds coming from the mansion. Sometime after 1:00 a.m., you were startled by the wail of sirens. The police called you into the mansion as possible witnesses to a murder. Because of your knowledge of mathematics, Inspector McFrito has asked you to write up a report of how you determined "whodunit?" and "when?"
You are to write a formal report to Inspector McFrito, giving a detailed explanation of how you arrived at your conclusion. All of your mathematical reasoning should be presented and justified. You are encouraged to discuss this problem with each other, but then each of you is to write up your report individually.
In writing up your solution, keep in mind that Inspector McFrito is mainly interested in your results. Your report should clearly and immediately state your results, then give supporting documentation. This may seem abrupt or rude since we are accustomed to beginning a letter with a personal greeting. A technical report or memo should start with the final result, then give supporting documentation, and finally close with a person greeting or expression of appreciation for being able to work on this project.
Although you are encouraged to work together to solve this problem, you are each to write up a report of the solution individually. During the next two weeks, we will continue with the ordinary class work of calculus. If you come to class with questions about this problem, you may use part of the class period for discussion of the problem.
Your paper for this project will be in the form of a business memo, written to Professor McFrito. Write your report on Math Iz Us letterhead stationary. It has been a long time since Inspector McFrito completed his last calculus class (and mathematics was not his strongest subject in school). He will need to be able to use the results you present in your report to make an arrest, and then to argue the case before the District Attorney. Explain your results clearly and professionally, so that the Inspector can quote you when he appears in court. Attach your calculations as an appendix to your memo, clearly showing how you calculated determined who should be charged with murder -- and how you can be sure that this accusation is correct. The formal memorandum should be word-processed, and does not need to be any more than two or three pages long. The appendix showing your calculations may be handwritten, and should be legible.
The audience for your paper: You are writing this report for the Inspector McFrito. Although he is quite knowledgeable about police matters and points of law, his calculus is a bit rusty (although he will not want you to mention this in a report that may be quoted as evidence in the trial). Write your report in professional manner, which gives him the technical arguments that he needs while also respecting his expertise. Remember that you are a professional who is being called upon by another professional, and your report will be used to determine legal penalties for the accused.
Your report will be graded on format, writing style, mathematical content and correctness, and evidence of synthesis and integration of the concepts.
Your report should make a good -- professional -- first impression. It should be word-processed, and should look like a professional memo. (Mathematical notations may be written in neatly by hand.)
Although the occassion requiring your services as a technical expert is a murder mystery, your report should not keep Inspector McFrito in suspense. In a report of this kind, it is important to give the result clearly and immediately, then include supporting documentation and calculations. Write your report simply, in standard English. Pay attention to grammar, spelling, and sentence structure. You should use a spell checker (or ask a friend to proof-read your report).
Your solutions should be mathematically correct. All of your mathematical reasoning should be presented and justified. Not only will the Inspector be interested in understanding your results himself, he may be called upon during the trial to explain the underlying reasoning in a court of law.
The depth of your responses to questions posed by this scenario will give an indication of how well you have internalized mathematical ideas about functions, rates of change, data collection, and Newton's Laws of Cooling.