This Modeling Scenario has an English and Spanish version.
An oil slick spreads at sea. From time to time, but irregularly, a helicopter is dispatched to photograph the oil slick. On each trip, the helicopter 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.
Build a model for the size of the oil slick at time t.
Predict the future size of the oil slick, say at t = 10 min, t = 20 min, t = 120 min.
Plot your model of the size of the oil slick as a function of time.
Find the time at which the oil slick is 8 square miles.
Determine the time of each of the observations for the first, third, fifth, and seventh initial observations.