You have been contracted by a pharmaceutical company to study the way that the body absorbs a new drug, and to help determine appropriate dosage information for this drug.
Study the information which is provided on the handout available in class on Wednesday, November 19. You are to compare two models for the rate at which the drug is eliminated from the body. Model A is a linear model, and Model B uses a differential equation. One of these models has been identified as being the more accurate one in clinical tests. You are to write a report of your findings answering the questions which are given on the handout. Your report should be presented as a formal memo on your professional letterhead stationary. (You can decide whether you work for a firm, or are in business for yourself. You might design a logo to represent your firm.)
Your formal report should be simply and clearly written. Your reader will be a professional working for the pharmaceutical firm, but may not have taken a recent course in calculus. (Very probably, such a professional would have had a course in calculus more than five years ago ... and might be a bit rusty on the details of calculus computations.) Your formal memorandum should be word processed, and does not need to be any more than three to five pages long. The descriptive text should be word processed, but you may write in your computations by hand. If you computations get involved and seem to distract from your presentation of the ideas in your formal memo, you may include these in a hand-written appendix.
You may work together on this project, but each of you is to write up your report individually. Your report is due on Wednesday, December 3.
The ideas that we are studying in Chapter 8 -- sequences and series -- are directly applicable to the solution of this problem. I do not plan to lecture about this problem, per se, but if you come to class with questions about this problem, we will take time to discuss your questions in class.
Your grade on this project will contribute about 5% to your grade for the course. As usual, I will use four criteria in marking this project: format or presentation, writing style, content or mathematical correctness, and evidence of synthesis or understanding.
Presentation / Format (10%): Your work should be make a good professional first impression. It should be wordprocessed. (Mathematical notations may be written in neatly by hand.) Your work should be presented with a cover letter, addressed to your contact person at the pharmaceutical company which has hired you to investigate this problem.
Writing Style (15%): Write your report in standard English, and pay attention to sentence structure. You should use a spell checker (and ask a friend to proof-read your work).
The cover letter for your report should simply and clearly answer the questions that have been posed in Part C of the handout. This cover letter should be clearly and simply written.
Content / Mathematical Correctness (60%): Your solutions should be mathematically correct. You should show enough of your work that your reader can easily understand how you got your results. Your detailed mathematical calculations should be included as an appendix or a supplement to your cover letter.