Concept explainers
Learning Curve A learning curve is a graph of a function P(t) that measures the performance of someone learning a skill as a function of the training time t. At first, the rate of learning is rapid. Then, as performance increases and approaches a maximal value M, the rate of learning decreases. It has been found that the function
where k and C are positive constants and C < M is a reasonable model for learning.
- (a) Express the learning time t as a function of the performance level P.
- (b) For a pole-vaulter in training, the learning curve is given by
where P(t) is the height he is able to pole-vault after t months. After how many months of training is he able to vault 12 ft?
- (c) Draw a graph of the learning curve in part (b).
(a)
The value of time
Answer to Problem 88E
The value of time
Explanation of Solution
Given:
Equation of
Calculation:
Simplify the equation (1),
Divide each side of above equation by C.
Take exponential both sides of above equation to evaluate
Hence, Value of time t is
(b)
The value of time
Answer to Problem 88E
The value of time
Explanation of Solution
Given:
Value of
Calculation:
Value of
Substitute 12s for
Take exponential both sides of above equation to evaluate
Hence, the value of time
(c)
To sketch: The graph of the function
Explanation of Solution
The given function is
Substitute 0 for
Substitute the different values of
t | P(t) |
0 | 6 |
23.3 | 12 |
10 | 8.987 |
The graph of function is give below,
Figure (1)
Hence, Figure (1) shows the graph of function
Chapter 4 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning