Writing Project 24:

Radioactive Decay and the Future

This is a project for a student who knows already what integrals are and who is able to read one or two chapters in the book before we treat it in class. It is intended only for students obtaining an "A" in this class with eyes closed, willing to take a challenge.

The power plant industry proposes four production curves for radiactive material for the future. For any of them, f(t) desribes how much material they want to produce in year t from now. Assume that 3% of the material decays in one year. The four functions are:

a) f₁(t) = 180*t
b) f₂(t) = 9000
c) f₃(t) = 9436*t/(t+1)
d) f₄(t) = 2458*ln(t+1)

(In each of the four models, the amount of material produced during the first 100 years is about the same).

a) How much radioactive material is still there (not yet decayed) after 50 years in each of the four models? You are not able to integrate all four functions by hand, but use MathCad.

b) The government will only allow models where the undecayed radioactive material will not grow without bound. Which of these four models is therefore not possible? Use again MathCad, but you can also reason without that.

Erich Prisner, August 2003