A model for learning is described by the differential equation 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). (Use P for P(t). Assume that P(0) = 0.) What is the limit of this expression as t increases without bound? lim t → ∞ P(t) =
A model for learning is described by the differential equation 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). (Use P for P(t). Assume that P(0) = 0.) What is the limit of this expression as t increases without bound? lim t → ∞ P(t) =
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 5CR
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A model for learning is described by the differential equation
| dP |
| dt |
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).
(Use P for P(t). Assume that
P(0) = 0.)
What is the limit of this expression as t increases without bound?
lim t → ∞ P(t) =
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