Problem 39 Hard Difficulty

In Exercise 9.1.15 we formulated a model for learning in the form of the differential equation
$ \frac {dP}{dt} = k(M - P) $
where $ P(t) $ measures the performance of someone learning a skill after a training time $ t, M $ is the maximum level of performance, and $ k $ is a positive constant. Solve this differential equation to find an expression for $ P(t). $ What is the limit of this expression?

Answer

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Video Transcript

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