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# 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?

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

#### Topics

Differential Equations

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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

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

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#### Topics

Differential Equations

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp