Describe the trend shown by the graph in Exercises in terms of learning new tasks. What happens initially and what happens as time increases?
Exercises
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.
How many learning trials are necessary for 0.95 of the responses to be correct? Identify your solution as a point on the graph.
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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