Unit 9

Sequences & Exponential Functions

Arithmetic/geometric sequences as functions, exponential growth & decay, linear vs. exponential

This unit is about patterns that grow in a steady way: number lists that climb by a fixed step, and the kind of growth behind money earning interest or a population doubling. It pays off because that second kind, growing by multiplying, shows up everywhere once you can spot it.

It helps to have one thing fresh: working out the value of an expression when you put a number into it. If you'd like a quick warm-up, redo a couple of problems on that from an earlier unit.

This is a shorter unit, and it rests on one idea you can hold in a single sentence. Some patterns grow by adding the same amount each step. Others grow by multiplying by the same amount each step. That one difference, add the same versus multiply the same, separates the two families you'll meet here, and it's the thing to keep in mind on every page.

You'll start with sequences, which are just ordered lists of numbers, because they make that contrast something you can count on your fingers. Then you'll meet exponential functions, which are the smooth, grown-up version of the multiplying pattern, and the kind of thing that describes money earning interest or a population doubling.

Before each new sitting, redo two or three problems from a lesson or two back from memory first. It's a small warm-up, and it does more for you than re-reading.