Chapter 4.1, Problem 45E

Psychologists have developed mathematical models to predict memory performance as a function of the number of trials $n$ of a certain task. Consider the learning curve

$P=\frac{0.5+0.9(n-1)}{1+0.9(n-1)},n>0$

where $p$ is the fraction of correct responses after $n$ trials.

(a) Complete the table for this model. What does it suggest?

(b) According to the model, what is the limiting percent of correct responses as $n$ increases?