Everyone Moves. The Total Holds.

You'll learnto predict how a population shifts between two places using a matrix.

Each year a share of the city leaves for the suburbs, and a share of the suburbs comes back. One matrix stores every one of those fractions, its columns reading off where each group started. Multiply, and the population takes a single step; multiply again for the next. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · STATES · COLUMNS · CONSERVATION · STEADY STATE · v4

Unit 4 is not assessed on the AP exam — it's here because the ideas are genuinely useful.

each column is one from-state, and every column adds to 1

Before you start

What you're looking at

A town drawn as two groups of figures, one for the city and one for the suburbs.

The question

If a share moves each way every year, where do the two counts end up?

Step 1 / 12