BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Solutions

Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Psychologists interested in learning theory study learning curves, A learning curve is the graph of a function P(t), the performance of someone learning a skill as a function of the training time t. The derivative dP/dt represents the rate at which performance improves.

  1. (a) When do you think P increases most rapidly? What happens to dP/dt as t increases? Explain.
  2. (b) If M is the maximum level of performance of which the learner is capable, explain why the differential equation

d P d t = k ( M P ) k a positive constant

is a reasonable model for learning.

  1. (c) Make a rough sketch of a possible solution of this differential equation.

(a)

To determine

To find: Time at which P increases most rapidly and to study the behavior of dPdt as t increases.

Explanation

At the beginning P increases most rapidly, it is reasonable to assume that one beginner learns more at starting time. Initially dPdt is very large

(b)

To determine

To explain: The differential equation dPdt=k(MP) is relevant model for learning.

(c)

To determine

To sketch: The possible solution of the differential equation.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Answers to Your Study Problems

Solve them all with bartleby. Boost your grades with guidance from subject experts covering thousands of textbooks. All for just $9.99/month

Get As ASAP
Sect-9.1 P-11ESect-9.1 P-12ESect-9.1 P-13ESect-9.1 P-14ESect-9.1 P-15ESect-9.1 P-16ESect-9.1 P-17ESect-9.2 P-1ESect-9.2 P-2ESect-9.2 P-3ESect-9.2 P-4ESect-9.2 P-5ESect-9.2 P-6ESect-9.2 P-7ESect-9.2 P-8ESect-9.2 P-9ESect-9.2 P-10ESect-9.2 P-11ESect-9.2 P-12ESect-9.2 P-13ESect-9.2 P-14ESect-9.2 P-19ESect-9.2 P-20ESect-9.2 P-21ESect-9.2 P-22ESect-9.2 P-23ESect-9.2 P-24ESect-9.2 P-27ESect-9.3 P-1ESect-9.3 P-2ESect-9.3 P-3ESect-9.3 P-4ESect-9.3 P-5ESect-9.3 P-6ESect-9.3 P-7ESect-9.3 P-8ESect-9.3 P-9ESect-9.3 P-10ESect-9.3 P-11ESect-9.3 P-12ESect-9.3 P-13ESect-9.3 P-14ESect-9.3 P-15ESect-9.3 P-16ESect-9.3 P-17ESect-9.3 P-18ESect-9.3 P-19ESect-9.3 P-20ESect-9.3 P-21ESect-9.3 P-22ESect-9.3 P-23ESect-9.3 P-24ESect-9.3 P-29ESect-9.3 P-30ESect-9.3 P-31ESect-9.3 P-32ESect-9.3 P-33ESect-9.3 P-34ESect-9.3 P-35ESect-9.3 P-36ESect-9.3 P-37ESect-9.3 P-38ESect-9.3 P-39ESect-9.3 P-40ESect-9.3 P-41ESect-9.3 P-42ESect-9.3 P-43ESect-9.3 P-44ESect-9.3 P-45ESect-9.3 P-46ESect-9.3 P-47ESect-9.3 P-48ESect-9.3 P-49ESect-9.3 P-50ESect-9.3 P-51ESect-9.3 P-52ESect-9.3 P-54ESect-9.4 P-1ESect-9.4 P-2ESect-9.4 P-5ESect-9.4 P-6ESect-9.4 P-7ESect-9.4 P-8ESect-9.4 P-9ESect-9.4 P-10ESect-9.4 P-11ESect-9.4 P-12ESect-9.4 P-13ESect-9.4 P-14ESect-9.4 P-16ESect-9.4 P-17ESect-9.4 P-18ESect-9.4 P-21ESect-9.4 P-22ESect-9.4 P-23ESect-9.4 P-24ESect-9.4 P-25ESect-9.5 P-1ESect-9.5 P-2ESect-9.5 P-3ESect-9.5 P-4ESect-9.5 P-5ESect-9.5 P-6ESect-9.5 P-7ESect-9.5 P-8ESect-9.5 P-9ESect-9.5 P-10ESect-9.5 P-11ESect-9.5 P-12ESect-9.5 P-13ESect-9.5 P-14ESect-9.5 P-15ESect-9.5 P-16ESect-9.5 P-17ESect-9.5 P-18ESect-9.5 P-19ESect-9.5 P-20ESect-9.5 P-21ESect-9.5 P-22ESect-9.5 P-23ESect-9.5 P-24ESect-9.5 P-25ESect-9.5 P-26ESect-9.5 P-27ESect-9.5 P-28ESect-9.5 P-29ESect-9.5 P-30ESect-9.5 P-31ESect-9.5 P-32ESect-9.5 P-33ESect-9.5 P-34ESect-9.5 P-35ESect-9.5 P-36ESect-9.5 P-37ESect-9.5 P-38ESect-9.6 P-1ESect-9.6 P-2ESect-9.6 P-3ESect-9.6 P-4ESect-9.6 P-5ESect-9.6 P-6ESect-9.6 P-7ESect-9.6 P-8ESect-9.6 P-10ESect-9.6 P-11ECh-9 P-1RCCCh-9 P-2RCCCh-9 P-3RCCCh-9 P-4RCCCh-9 P-5RCCCh-9 P-6RCCCh-9 P-7RCCCh-9 P-8RCCCh-9 P-9RCCCh-9 P-1RQCh-9 P-2RQCh-9 P-3RQCh-9 P-4RQCh-9 P-5RQCh-9 P-6RQCh-9 P-7RQCh-9 P-1RECh-9 P-2RECh-9 P-3RECh-9 P-4RECh-9 P-5RECh-9 P-6RECh-9 P-7RECh-9 P-8RECh-9 P-9RECh-9 P-10RECh-9 P-11RECh-9 P-12RECh-9 P-13RECh-9 P-14RECh-9 P-15RECh-9 P-16RECh-9 P-17RECh-9 P-18RECh-9 P-19RECh-9 P-20RECh-9 P-21RECh-9 P-22RECh-9 P-23RECh-9 P-24RECh-9 P-1PCh-9 P-2PCh-9 P-3PCh-9 P-4PCh-9 P-5PCh-9 P-6PCh-9 P-7PCh-9 P-8PCh-9 P-9PCh-9 P-10PCh-9 P-11PCh-9 P-12PCh-9 P-13PCh-9 P-14PCh-9 P-15P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

For the supply equations in Exercises 61-64, where x is the quantity supplied in units of a thousand and p is t...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach