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.) -kt p(t) = - Me + M What is the limit of this expression as t increases without bound? lim P(t) M t∞ Consider the following. x= |t|, y = = |3 - Itl (a) Eliminate the parameter to find a Cartesian equation of the curve. 3−x, x ≥0| (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. У x x x 3 3 y 3 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.) -kt p(t) = - Me + M What is the limit of this expression as t increases without bound? lim P(t) M t∞ Consider the following. x= |t|, y = = |3 - Itl (a) Eliminate the parameter to find a Cartesian equation of the curve. 3−x, x ≥0| (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. У x x x 3 3 y 3 x
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 20E
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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.)
-kt
p(t)
=
-
Me + M
What is the limit of this expression as t increases without bound?
lim P(t)
M
t∞
Transcribed Image Text:Consider the following.
x= |t|,
y =
= |3
- Itl
(a) Eliminate the parameter to find a Cartesian equation of the curve.
3−x, x ≥0|
(b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.
У
x
x
x
3
3
y
3
x
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