I'm honestly not sure if this is a calculus question as much as it is a biology question, but I figured MSE will tell me either way.
If I inhale 100 units of smoke, I will exhale less than that amount. Say, for example, that I still have 5 units in my lungs. When I inhale and exhale again there will be some proportion of that 5 units left and so on. How much smoke, as a proportion of the initial 100 units, do I still have inside me after $n$ subsequent breaths?
EDIT: we concluded that the amount of smoke left in the lungs after $n$ breaths is in the form $S^{-n}$. Is there some means of now finding $S$? Surely now we are closer to the realm of biology than maths.
Look at it in terms of concentration: after taking one breath, the amount of smoke remaining is $\frac1{20}$ of the amount that was there before the breath. So after $n$ breaths, the proportion of smoke remaining to the initial amount of smoke is $\frac1{20^n}$.
Exactly this kind of problem comes up in chemistry, when an initial stock solution is serially diluted and the final concentration (i.e. molarity) must be calculated.