Writing Project

The following group project is to be worked on by no more than fourstudents. You may use any materials you think may be useful in solving the problems but you may not ask anyone for help other than the people you have chosen to work with. This means you may not ask a tutor or any person other than those in your immediate group for help.

You are to type a response to the problem presented backing up your conclusions with mathematical reasoning, formulas, and solutions. Your grade will depend on how well you communicate your response as well as the accuracy of the conclusions. This project will be scored using the rubric on the last page of this document.

Please sign and date here to indicate that you have read and agree to abide by the above mentioned stipulations.

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Student Name #1Date

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Student Name #2Date

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Student Name #3Date

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Student Name #4Date

11 Patinkin Way

First National Park of Guilder

October 24th, 2000

MAT 221/216 Calculus Students

Chandler-Gilbert Community College

Mesa, AZ 85212

Dear Calculus Creators:

Things have finally quieted down around Guilder since Prince Humperdinck was kicked out of Florin. The good news is that I've managed to find a government job as the head of the First National Park of Guilder. The bad news is that most of the Park consists of the Fire Swamp. The worst news is that the only other employee at the Park is Fezzik. Don't get me wrong, I love the giant like a brother, but he can be a little frustrating to work with. When I went looking for help with our long range planning, your enterprising and resourceful professor naturally referred me to you.

We have two species that have me really worried about the future of the Park: the indigenous ROUS (rodents of unusual size) and the BTS (Brown Tree Snakes) which entered Guilder about 50 years ago as a stowaway from Guam on the ship of the Dread Pirate Roberts. Fortunately, ROUS's eat BTS’s. Unfortunately, BTS’s reproduce very rapidly.

My predecessor at the Park was a meticulous census taker (who used statistical sampling, by the way, to get more accurate counts), so I have approximate populations for each species for the last 30 years.

Year / BTS’s / ROUS's
1970 / 15300 / 415
1972 / 9890 / 910
1974 / 2860 / 950
1976 / 3340 / 525
1978 / 9340 / 250
1980 / 12290 / 460
1982 / 9050 / 830
1984 / 4840 / 855
1986 / 5130 / 545
1988 / 8720 / 340
1990 / 10490 / 500
1992 / 8550 / 770
1994 / 6030 / 790
1996 / 6200 / 560
1998 / 8350 / 410
2000 / 9410 / 525

It looks like the populations are following some sort of pattern, but I'm not sure what it is. My real problem is that when either population gets very large, I will need additional employees to make sure that both species stay within the park and don't escape in the Guilder farmland. This is where I need your expert help. Specifically, I need a prediction for what the populations will be in each of the next 20 years. As a side note, after the Dread Pirate Roberts killed the extremely intelligent (and a bit conceded) Vizzini by poisoning him in a dual of wits, I found the mathematical equations given below on his person. Since Vizzini was formerly the accountant for the First National Park of Guilder, I am wondering if they have anything to do with the ROUS and BTS populations.



I believe the populations are fluctuating less and less, and may eventually stabilize. I would like your expert opinion on whether or not the populations do stabilize, and if they do, I need to know how long it will take and what the eventual populations will be.

Once the populations stop fluctuating so drastically, we will be able to dramatically improve access to the Park by offering summer camps, establishing permanent camp grounds, and perhaps even adding a log ride, although there are still some flame-retardant issues to be worked out. This should all be possible when the ROUS population is fluctuating by less than 75 per year and the BTS population is fluctuating by less than 500 per year. As usual, I need your expert recommendation on when this will occur. Finally, I would appreciate it if you would determine if there seems to be any point in time(s) when the rate of population growth is zero for both species.

I have a meeting with the Budget Advisory Committee at the end of the month to propose our budget for the next two decades, so I would greatly appreciate your report by October 31st, 2000.

Gratefully yours,

Inigo Montoya

P.S.

A Few Helpful Hints From Your Professor

To see the general trend of the populations, I would suggest plotting the points for each population separately, with time on the horizontal axis and population on the vertical axis. It may make things a little bit easier if you let time t=0 be 1970. Be sure to use the tools and proper notation of Calculus in your reply (i.e. limits, rate of change, derivatives, tables, graphs, etc.)

Checklist for Your Writing Project

Directions:

  • Please attach this page with a paper-clip to your writing assignment when you turn it

in.

  • This list will be used to grade your assignment, and will be returned to you with

comments.

  • Please feel free to use this checklist as a guide for yourself while writing the

assignment.

Does this paper:

  1. Clearly summarize the problem to be solved?
  2. Provide a paragraph which explains how the problem will be approached?
  3. State the answer in a few complete sentences which stand on their own?
  4. Give a precise and well-organized explanation of how the answer was found,

including:

  • algebraic support
  • graphical support
  • numerical support

as appropriate?

  1. Clearly label diagrams, tables, graphs, or other visual representations of the

math?

  1. Define all variables, terminology, and notation used?
  2. Clearly state the assumptions which underlie the formulas and theorems, and

explain how each formula or theorem is derived, or where it can be found?

  1. Give acknowledgment where it is due?
  2. Use correct spelling, grammar, and punctuation?
  3. Contain correct mathematics?
  4. Solve the problem(s) that were originally asked?

Instructor Comments:

Your group’s score out of 50 points is ______.

1

Trey Cox and Scott Adamson ©2000