In the Preview of Calculus at the start of our textbook, we were introduced to Zeno of Elea, the 5th century BC philosopher as well as his paradoxes. Recall that Zeno claimed it must be impossible to ever reach a wall, since you must first walk half the distance to the wall, then half this distance, and half that distance, and so-on. Since it would take an infinite number of halvings, Zeno reasoned, it would take an infinite amount of time to ever reach the wall. While such thought experiments sometimes seem irrelevant to "real life", there are several real physical situations that mirror the issues surrounding Zeno's Paradoxes. Take, for example, the radioactive decay of carbon. A naturally occurring isotope of Carbon-14, 14C, has a half-life of 5,730 years. This means that after every 5,730 years, about half of the 14C atoms in a sample will decay into Carbon-12, 12C. If you wait another 5,730 years the number of remaining 14C atoms will halve again.

This is very similar to Zeno's Paradox and raises some interesting questions.

1. We all know that you will easily reach the wall in Zeno's Paradox, but it is less clear whether all of the 14C isotopes in a sample will eventually decay. What, if anything, is different between these two situations?

2. What if you started with just one 14C atom. What do you think happens then?

3. Relate this to your Unit 1 Activity with the pennies. What is different about your experiment from this other real-life scenario?

4. How can we compare the two to any other real-life example of exponential decay?