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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

$$\lim _{t \rightarrow \infty} P(t)=M-M \cdot 0=M$$

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AM

Anaitl M.

March 10, 2021

A sphere with radius 1 m has temperature 11°C. It lies inside a concentric sphere with radius 2 m and temperature 19°C. The temperature at a distance r from the common center of the spheres satisfies the differential equation below. If we let S = dT/dr, t

Video Transcript

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