STATEMENT OF PROBLEM

An oil-slick spreads at sea. From time to time, but irregularly, a helicopter is dispatched. On each trip, it arrives over the slick, the pilot takes a picture, waits 10 minutes, takes another, and heads home. On each of seven trips the size (in area) of the slick is measured from both photographs. The data is offered below.

Area of Slick (square miles)

Initial 10 Minutes
Observation Later
1.047 1.136
2.005 2.085
3.348 3.415
5.719 5.762
7.273 7.301
8.410 8.426
9.117 9.126

(1) Build a model for the growth of the oil-slick. We need a model we
can use to predict the size of this slick beyond the observations and we
see this as a part of a larger study of oil slick spread.
(2) Confirm that your model is a reasonable one for predicting the growth
of this oil slick.
(3) Determine what your model predicts as the long term growth of this
oil slick.
(4) Discuss weaknesses, attention to reality, and assumptions you had to
make in your model.