Formulas with rational expressions are often used to model learning. Many of these formulas model the proportion of correct responses in terms of the number of trials of a particular task. One such model, called a learning curve, is where P is the proportion of correct responses after x trials. If P = 0, there are no correct responses. If P = 1, all responses are correct. The graph of the rational formula is shown. Use the formula to solve Exercises 103–104.

How many learning trials are necessary for 0.5 of the responses to be correct? Identify your solution as a point on the graph.

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Proportion of Correct Responses P 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 A Learning Curve P = 0.9x 0.4 0.9x + 0.1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Number of Learning Trials X