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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?

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Calculus 2 / BC

Chapter 9

Differential Equations

Section 3

Separable Equations

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

Missouri State University

Harvey Mudd College

Idaho State University

Lectures

13:37

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

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