Lesson 9 introduced activation — a number capturing how easily a declarative chunk can be retrieved — without saying where the number comes from. ACT-R’s answer has two ingredients.
Base-level activation tracks how often and how recently a chunk has been used. The simplified single-use form:
B = −d · ln(t)
where t is time since the chunk was last retrieved, and d is a decay rate (ACT-R’s usual default is d = 0.5). Bigger t (longer since you used it) → more negative B → weaker, slower, less reliable retrieval. Every additional retrieval of a chunk also boosts it — practiced facts resist decay better than one-off facts, which is why the full formula sums a term like this over every past use — but for one use, this simplified version is exact.
Spreading activation is the second ingredient: a chunk’s total activation also rises when related chunks currently in the goal/context are active — recalling “chess” makes chess-adjacent chunks (openings, your last opponent, the Sicilian Defense) easier to retrieve too, the same way one memory cues another. Base-level activation asks “how used is this, on its own”; spreading activation asks “how connected is this to what I’m thinking about right now.”
A chess player memorized a rare opening name (the “Grünfeld Defense”) and hasn’t thought about it since — t = 16 days. Using the base-level formula with d = 0.5, compute B.