Concept explainers
To sketch: The solution curve that passes through the point (1000, 40).
Answer to Problem 9E
The solutioncurve matches the curve obtained from the direction field.
Explanation of Solution
Given information:
Consider the following differential equation which models the rabbit and wolf population:
Formula used:
The graph is plotted against x axis and y axis.
Calculation:
Where W and R are the population of which and rabbit respectively
This differential equation can be written as:
Now integrate on both sides to get:
Using the property a In (x) = In xa, one can write:
Then,
Where c is a constant
When the curve of the implicit plot passes through (1000, 40) , the value of the constant c is:
So the equation of a curve passing through (1000,40)will be:
For the implicit plot in maple, use the following commands:
with (plots, implicitplot)
Then the plot will be:
The solutioncurve matches the curve obtained from the direction field.
Conclusion:
The solutioncurve matches the curve obtained from the direction field.
Chapter 7 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced 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