Modeling with differential equations is a multistage process. In this scenario, we use Carbon-14 dating of the Dotsero volcano in Colorado as a way of emphasizing this multistage process. Beginning with a scenario of interest, a specific and measurable problem statement is proposed. Students research how radiocarbon dating works and list relevant assumptions. A compartment diagram and corresponding word equation are then identified and used to develop an appropriate initial value problem. Students solve the IVP analytically using separation of variables and numerically using Euler's method. For the numerical solution, students can adapt programs that are provided using Python and R, but spreadsheet or calculator solutions can also be used. The analytical and numerical solutions are then used to determine the eruption date of the volcano. Finally, students provide a discussion of the results in light of the information given and assumptions made.