Homework Help is Here – Start Your Trial Now!
Math
Calculus
Problem 3. A Holling's Type III response is similar to Type II since it assumes that the consumer is limited by its ability to process/handle food. However, Type III additionally assumes that at low food densities, consumption accelerates as food density increases. A Holling's Type III functional response can be modeled by the equation 10. C(x) 2ax² 1+ abx2 find sec. denvance Piale = 0, solve forx where a represents the rate at which the consumer encounters food and b is the average amount of time a consumer spends processing the food. a) Show that C(x) is increasing for all x > 0; that is, show that C'(x) > 0 for all x > 0. b) Show that C(x) is accelerating for low food densities and decelerating for large food densities. To do this, find a value x = a such that C"(a) = 0, C'(x) > 0 for 0 < x a.

Problem 3. A Holling's Type III response is similar to Type II since it assumes that the consumer is limited by its ability to process/handle food. However, Type III additionally assumes that at low food densities, consumption accelerates as food density increases. A Holling's Type III functional response can be modeled by the equation 10. C(x) 2ax² 1+ abx2 find sec. denvance Piale = 0, solve forx where a represents the rate at which the consumer encounters food and b is the average amount of time a consumer spends processing the food. a) Show that C(x) is increasing for all x > 0; that is, show that C'(x) > 0 for all x > 0. b) Show that C(x) is accelerating for low food densities and decelerating for large food densities. To do this, find a value x = a such that C"(a) = 0, C'(x) > 0 for 0 < x a.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
Problem 3. A Holling's Type III response is similar to Type II since it assumes that the consumer is limited by its ability to process/handle food. However, Type III additionally assumes that at low food densities, consumption accelerates as food density increases. A Holling's Type III functional response can be modeled by the equation C(x) = 2ax² 1+ abx² NOT.. find sec. denvance piale = 0, solve where a represents the rate at which the consumer encounters food and b is the average amount of time a consumer spends processing the food. a) Show that C(x) is increasing for all x > 0; that is, show that C'(x) > 0 for all x > 0. b) Show that C(x) is accelerating for low food densities and decelerating for large food densities. To do this, find a value x = a such that C"(a) = 0, C'(x) > 0 for 0 < x <a, and C'(x) < 0 for x > a.
Transcribed Image Text:Problem 3. A Holling's Type III response is similar to Type II since it assumes that the consumer is limited by its ability to process/handle food. However, Type III additionally assumes that at low food densities, consumption accelerates as food density increases. A Holling's Type III functional response can be modeled by the equation C(x) = 2ax² 1+ abx² NOT.. find sec. denvance piale = 0, solve where a represents the rate at which the consumer encounters food and b is the average amount of time a consumer spends processing the food. a) Show that C(x) is increasing for all x > 0; that is, show that C'(x) > 0 for all x > 0. b) Show that C(x) is accelerating for low food densities and decelerating for large food densities. To do this, find a value x = a such that C"(a) = 0, C'(x) > 0 for 0 < x <a, and C'(x) < 0 for x > a.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS