Learning curves are studied by psychologists interested in the theory of learning. A learning curve is the graph of a function PI(f) that represents the performance level of someone who has trained at a skill or t hours. Thus, the I represents the rate at which the performance level improves. By convention, at he derivative PL(f) is taken to be a positive function. f M (a positive constant) is the maximum performance level of which the learner is capable, then which differential equations could be a reasonable model for learning (or more precisely, performance level)? Jse your common sense applied to the practical meaning behind each equation to determine which of che following are reasonable. = k(M-PI) for some positive constant k at dPI I. k(PL) for some positive constant k dt dPI I. dt k(M-PI)1/2 for some positive constant k dPI V. åt %3D (M-Pr) for some positive constant k O I only O I and II only O III only O I and III only O IV only

Learning curves are studied by psychologists interested in the theory of learning. A learning curve is the graph of a function PI(f) that represents the performance level of someone who has trained at a skill or t hours. Thus, the I represents the rate at which the performance level improves. By convention, at he derivative PL(f) is taken to be a positive function. f M (a positive constant) is the maximum performance level of which the learner is capable, then which differential equations could be a reasonable model for learning (or more precisely, performance level)? Jse your common sense applied to the practical meaning behind each equation to determine which of che following are reasonable. = k(M-PI) for some positive constant k at dPI I. k(PL) for some positive constant k dt dPI I. dt k(M-PI)1/2 for some positive constant k dPI V. åt %3D (M-Pr) for some positive constant k O I only O I and II only O III only O I and III only O IV only

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.3: Modeling Data With Linear Functions

Problem 17E: Later High School Graduates This is a continuation of Exercise 16. The following table shows the...

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

Learning curves are studied by psychologists interested in the theory of learning. A learning curve is the
graph of a function PL(f) that represents the performance level of someone who has trained at a skill
for t hours. Thus, the I represents the rate at which the performance level improves. By convention,
the derivative PL(t) is taken to be a positive function.
If M (a positive constant) is the maximum performance level of which the learner is capable, then which
differential equations could be a reasonable model for learning (or more precisely, performance level)?
Use your common sense applied to the practical meaning behind each equation to determine which of
the following are reasonable.
dPL = k(M- PL)
dt
I.
dt
for some positive constant k
II.
dPI
= k(PL) for some positive constant k
III.
= k(M-PI)l/2 for some positive constant k
åt
dP L
IV.
at
(M-PI)
-for some positive constant k
O I only
O I and II only
O III only
O I and III only
O IV only

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