Mistake Master
Mistake Master · AP Precalculus · Unit 4 · Step-Through Animation
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. Watch where the shares finally stop moving.
Unit 4 is not assessed on the AP exam — it's here because the ideas are genuinely useful.
columns are from-states · next state = M × current column state
Before you start
What you're looking at
Person icons moving between a labeled city and suburbs, before any percentages appear.
The question
Where will the population be next year?
Watch for
Movement turned into fractions and matrix columns — a column is where people started, a row is where they ended, so entry aij is the fraction going from state j to state i. That is one convention of two; others put from-states in the rows.
Step 1 / 8