One special characteristic of any exponential growth or decay function f(t) = Ab[superscript t] is its unique doubling time or half-life, each of which depends only on the base "b". The half-life is used to characterize the rate of decay of any radioactive substance or the rate at which the level of a medication in the bloodstream decays as it is washed out of the body by the kidneys, the liver, or both, depending on the drug. One can see these facts formally by applying the definitions of doubling time and half-life on the drug. This article looks at the notions of doubling time and half-life in greater depth, particularly in the context of whether they make any sense with nonexponential families of functions. (Contains 7 figures.)