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a. The expected 15 are enough for both the "very easy" and the "easy" group and so we can expect a total of 10+20=30 to show up.

b. The 41 from last week will inspire the average folks to turn out AND the easy and the very easy so next week we will see 10+20+40=70. This number will also inspire the hard so we will get 70+20 the following week. But the total of 90 will not inspire anyone in the very hard category so the number will stay at 90.

c. Last week's 91 won't be enough to inspire the very hard so we will see a drop to 90.

Checklist

1. This is a Schelling critical mass model. Schelling is a contemporary economist who was born in Oakland in 1921. He won the Nobel prize in 2005 for "having enhanced our understanding of conflict and cooperation through game-theory analysis" (Wikipedia).
2. These models describe situations where a behavior decision is based on the numbers of others who have or are expected to engage in some behavior
3. Examples could include joining a protest, buying a product, adopting an opinion…
4. The bottom row of numbers represents frequencies - how many people at each threshold level. A threshold level is how many people you need to expect to show up for you to decide to show up.
5. Explain that can be analyzed graphically by starting with frequency histogram and converting to a cumulative frequency diagram that will likely take form of an S curve. With a 45 degree line on the chart we can identify stable and unstable equilibria.
6. See above.