(d) From the graph it should be apparent that there is a limit to the amount of food consumed as more and more vegetation is available. Find this limiting value of C. C = (               ) lbs

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section1.8: Interpreting Graphs Of Functions
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(d) From the graph it should be apparent that there is a limit to the amount of food consumed as more and more vegetation is available. Find this limiting value of C.


C = (               ) lbs

The amount C of food consumed in a day by a sheep is a function of the amount V of vegetation available, and a model is
3V
C=.
50 + V
Here Cis measured in pounds and V in pounds per acre. This relationship is called the functional response.
(a) Make the graph of C versus V. Include vegetation levels up to 1000 pounds per acre.
5
3
2
2
200
400
600
800
1000
200
400
600
800
1000
3.0}
2.5
3
2.0
1.5
2
1.0
0.5
200
400
600
800
1000
200
400
600
800
1000
(b) Calculate C(600). (Round your answer to three decimal places.)
C(600)
= 2.769
Explain in practical terms what your answer means.
O C(600) represents the amount of food a sheep will consume when 600 pounds per acre of vegetation is available.
O C(600) represents the amount of vegetation available when a sheep consumes 600 pounds of food.
(c) Is the graph concave up or concave down?
concave up
concave down
Explain in practical terms what this means.
OAs the amount of vegetation available increases, the amount of food consumed decreases at a decreasing rate.
OAs the amount of vegetation available increases, the amount of food consumed increases at an increasing rate.
O As the amount of vegetation available increases, the amount of food consumed decreases at an increasing rate.
OAs the amount of vegetation available increases, the amount of food consumed increases at a decreasing rate.
(d) From the graph it should be apparent that there is a limit to the amount of food consumed as more and more vegetation is available. Find this limiting value of C.
Ib
G an deg
Transcribed Image Text:The amount C of food consumed in a day by a sheep is a function of the amount V of vegetation available, and a model is 3V C=. 50 + V Here Cis measured in pounds and V in pounds per acre. This relationship is called the functional response. (a) Make the graph of C versus V. Include vegetation levels up to 1000 pounds per acre. 5 3 2 2 200 400 600 800 1000 200 400 600 800 1000 3.0} 2.5 3 2.0 1.5 2 1.0 0.5 200 400 600 800 1000 200 400 600 800 1000 (b) Calculate C(600). (Round your answer to three decimal places.) C(600) = 2.769 Explain in practical terms what your answer means. O C(600) represents the amount of food a sheep will consume when 600 pounds per acre of vegetation is available. O C(600) represents the amount of vegetation available when a sheep consumes 600 pounds of food. (c) Is the graph concave up or concave down? concave up concave down Explain in practical terms what this means. OAs the amount of vegetation available increases, the amount of food consumed decreases at a decreasing rate. OAs the amount of vegetation available increases, the amount of food consumed increases at an increasing rate. O As the amount of vegetation available increases, the amount of food consumed decreases at an increasing rate. OAs the amount of vegetation available increases, the amount of food consumed increases at a decreasing rate. (d) From the graph it should be apparent that there is a limit to the amount of food consumed as more and more vegetation is available. Find this limiting value of C. Ib G an deg
Expert Solution
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The graph becomes horizontal at C=3.

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