Note on the power law of forgetting

Power functions (e.g., f(t) = at) describe the relationships among many variables observed in nature. One example of this is the power law of forgetting: The decline in memory performance with time or intervening events is well fit by a power function. This simple functional relationship accounts for a great deal of accumulated data. In this note, we consider a simple yet general memory model in which all items decay monotonically in strength, but at different rates. To translate between continuous changes in strength and actual memory for events we assume a simple strength threshold for remembering. We prove a limit theorem for this model: as time grows large and memories decay, the empirical forgetting function approaches a power function under very general conditions. Power forgetting emerges for almost any monotonically decreasing strength function (including linear and exponential cases). We also illustrate by way of simulations that the power function provides an excellent fit to the entire time-course of the forgetting function, not just its limiting behavior.