Most of these terms (exposition, rising action, climax, falling action, and resolution) are the general sections of any story. They help you organize a story in your mind and visualize it as a structured set of events.
Although I'll say that, for example, the exposition of The Cay is Chapters 1-2, and that the rising action is Chapters 3-11 and so on, other readers might have slightly different ways to make those divisions. But the general idea is that these terms help us make a map of the plot in order to understand it.
First, the exposition of any story is the very beginning, where we learn what the setting is, who the characters are, and what they basically want.
So, you can find the exposition of The Cay in Chapters 1 and 2, when Phillip and his parents are wondering whether they should try to leave their Dutch island of Curacao to head to Virginia, where it might be safer. We learn that World War II is going on, and that there are shortages of food and water where Phillip is.
(The entire section contains 695 words.)