We describe a modelling activity for students in a course in which modelling with differential equations is appropriate. We have used this model in our coursework for years and have found that it enlightens students as to the model building process and parameter estimation for a linear, first-order, ordinary differential equation. The activity also provides a lesson in "knowing what to do when you do not know what to do." [G. Polya, "How to Solve It", Princeton University Press, Princeton, NJ, 1945]. (Contains 4 tables and 5 figures.)