This chapter describes several everyday situations and real-world phenomena that are modeled with first-order differential equations. The first one is a practical application that takes place in an orange juice processing plant. Briefly, the problem is to determine the percentage by weight of soluble solids (sugars, acids, etc.) in a large tank of orange juice concentrate at any given time if water is pumped into the tank while the concentrate is pumped out of the tank at the same rate. This is referred to as the orange juice problem in this chapter. It serves as an introduction to a modeling technique known as compartmental analysis. A one-compartment system consists of a single compartment that contains a particular type of matter or some species of animal or plant, where the matter or organism enters and leaves the compartment at known rates. Some examples are: farm-raised catfish in a man-made pond, E. coli bacteria growing in a flask of nutrient broth, carbon monoxide in a house, and money in a savings account. The orange juice problem is worked out in detail since it will serve as a paradigm for real-world phenomena that can be viewed as one-compartment systems. One of them is the radioactive decay law, which is derived using the hypothesis advanced by two Austrian physicists in the early 1900s that radioactive-decay processes are statistical in nature. Two other models that are also derived using compartmental analysis are the Malthusian and logistic models of population growth. These are well-known models from mathematical biology for predicting the populations of certain species of animals, such as fish in a pond, and other organisms, such as E. coli bacteria. The chapter concludes with a detailed explanation of how to compute the balance of a deposit account, such as a savings or money market account, where the accrued interest is credited to the account periodically. This will prepare the way for one of the topics in Chapter 7, where it is shown how to set up a one-compartment model of a loan, such as a car loan or a home mortgage, in order to model the amortization of the loan using a differential equation and the Dirac delta function, which is also introduced in Chap. 7 .