Hermann Ebbinghaus (1850 =1909) pioneered the study of memory. A 2011 article in the Journal of Mathematical Psychology presents the mathematical model R(t) = a + b(1 + ct)^–β for the Ebbinghaus forgetting curve, where R(t) is the fraction of memory retained t days after learning a task; a, b, and c are experimentally determined constants between 0 and 1; β is a positive constant; and R(0) = 1. The constants depend on the type of task being learned.

(a) What is the rate of change of retention t days after a task is learned?

(b) Do you forget how to perform a task faster soon after learning it or a long time after you have learned it?

(c) What fraction of memory is permanent?