In regulatory or decision-making contexts related to carcinogenic hazards, one would like to know the extra risks associated with various levels, durations, and ages of exposure to a carcinogen. To supply that information, quantitative risk assessments are required that make extrapolations on variables related to dose levels, timing of exposure, and age. Quantitative models that express age-specific mortality rates as functions of the exposure pattern and that allow such extrapolations to be made are presented. The uncertainty inherently associated with those extrapolations is discussed and is found to be exacerbated by small data sets and inadequate data availability. Specific examples are provided that involve asbestos-induced mesothelioma and leukemia caused by benzene exposure.