Fire Swamps and Rodents and Snakes (Oh, My)

11 Patinkin Way
First National Park of Guilder
September 16, 1998

Math 101 Students
Wheaton College
Norton, MA 02766
Dear Calculus Students:

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 worse 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 brown tree snake which entered Guilder about 50 years ago as a stowaway from Guam on the ship of the Dread Pirate Roberts . Fortunately, ROUS's eat brown tree snakes. Unfortunately, brown tree snakes 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 Tree Snakes ROUS's
1968 15300 415
1970 9890 910
1972 2860 950
1974 3340 525
1976 9340 250
1978 12290 460
1980 9050 830
1982 4840 855
1984 5130 545
1986 8720 340
1988 10490 500
1990 8550 770
1992 6030 790
1994 6200 560
1996 8350 410
1998 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 (which your enterprising and resourceful professor assures me you can deliver). Specifically, I need a prediction for what the populations will be in each of the next 20 years.

In addition, 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 logride, 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 brown tree snake population is fluctuating by less than 500 per year. As usual, I need your expert recommendation on when this will occur.

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 September 23.

Gratefully yours,
Inigo Montoya

A Few Notes from Your Enterprising and Resourceful 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 1968.