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 P(t) t→ ∞ = Find the orthogonal trajectories of the family of curves. y² = kx³ Graph several members of each family on a common screen. y x -5 5 -5 x 5 5 5 x 5 -5 x
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 P(t) t→ ∞ = Find the orthogonal trajectories of the family of curves. y² = kx³ Graph several members of each family on a common screen. y x -5 5 -5 x 5 5 5 x 5 -5 x
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter3: Linear And Nonlinear Functions
Section3.1: Graphing Linear Functions
Problem 19PPS
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Transcribed Image Text: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 P(t)
t→ ∞
=
Transcribed Image Text:Find the orthogonal trajectories of the family of curves.
y² = kx³
Graph several members of each family on a common screen.
y
x
-5
5
-5
x
5
5
5
x
5
-5
x
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