Fire Swamps and Rodents and Snakes (Oh, My)
11 Patinkin Way
First National Park of Guilder
September 16, 1998
Math 101 Students
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
| 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
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
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.
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.