Psychologists interested in learning theory study learning curves. A learning curve is a graph of a function P (t), the performance of someone learning a skill as a function of the training time t. The derivative dP/dt represents the rate at which performance improves,

 

1. Plot the solution over time. Decide the unit of time and explain why it is most suitable for this model. 

 

1. Using your habits as the model, create a table for 3 different values of M, and plot your learning curve. Using a graphing tool to generate the graph

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Learning Curve The management at a certain factory has found that a worker can produce at most 30 units in a day. The learning curve for the number of units N produced per day after a new employee has worked t days is

After 20 days on the job, a particular worker produces 19 units.

(a) Find the learning curve for this worker.

(b) How many days should pass before this worker is producing 25 units per day?

Learning Curve The management at a certain factory has found that the maximum number of units a worker can produce in a day is 75. The rate of increase in the number of units N produced with respect to time t in days by a new employee is proportional to 

(a) Determine the differential equation describing the rate of change of performance with respect to time.

(b) Solve the differential equation from part (a).

(c) Find the particular solution for a new employee who produced 20 units on the first day at the factory and 35 units on the twentieth day.