One of the early accomplishments of calculus was predicting the future position of a planet from its present position and velocity. Today this is just one of many situations in which we deduce everything we need to know about a function from one of its known values and its rate of change. From this kind of information, we can tell how long a sample of radioactive polonium will last; whether, given current trends, a population will grow or become extinct; and how large major league baseball salaries are likely to be in the year 2020. In this chapter, we examine the analytic, graphical, and numerical techniques on which such predictions are based. (Taken from an excerpt in the fifth edition of the Finney, Demana, Waits, Kennedy, and Bressoud textbook Calculus - Graphical, Numerical, Algebraic.)