The biological relationship between the growth for the fish population and the size of the fish population is g= 15S(1-S/5) where g is the growth of the fish population and S is the size of the population. The size of the harvest is a function of the amount of human effort expended b = 3ES where E is the level of effort. Market price of fish per unit is $100 and a constant marginal cost of effort is $50. The equation representing a sustainable harvest/catch level, b s, in S is b s = S(1 - S/ ).
The biological relationship between the growth for the fish population and the size of the fish population is g= 15S(1-S/5) where g is the growth of the fish population and S is the size of the population. The size of the harvest is a function of the amount of human effort expended b = 3ES where E is the level of effort. Market price of fish per unit is $100 and a constant marginal cost of effort is $50. The equation representing a sustainable harvest/catch level, b s, in S is b s = S(1 - S/ ).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Biological Relationship in Fish Population Dynamics**
The text explains the dynamics between fish population growth and various economic factors.
**Growth Relationship:**
The growth of the fish population is described by the equation:
\[ g = 15S(1 - S/5) \]
- *g* represents the growth of the fish population.
- *S* is the current size of the fish population.
**Harvest Size:**
The harvest size depends on human fishing efforts:
\[ b = 3ES \]
- *b* is the size of the harvest.
- *E* denotes the level of human effort expended.
**Economic Considerations:**
- The market price of fish per unit is $100.
- The constant marginal cost of effort is $50.
**Sustainable Harvest Equation:**
To maintain a sustainable level of harvesting, the equation in terms of population size \( S \) is:
\[ b_s = \text{(blank)} S(1 - S/\text{(blank)}) \]
The blank spaces would be filled with the appropriate values or expressions to complete the equation in educational content.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf605b71-789d-48e0-8055-d8207016854b%2F67b969f2-c80c-4024-955a-110735283572%2Fd5tgjo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Biological Relationship in Fish Population Dynamics**
The text explains the dynamics between fish population growth and various economic factors.
**Growth Relationship:**
The growth of the fish population is described by the equation:
\[ g = 15S(1 - S/5) \]
- *g* represents the growth of the fish population.
- *S* is the current size of the fish population.
**Harvest Size:**
The harvest size depends on human fishing efforts:
\[ b = 3ES \]
- *b* is the size of the harvest.
- *E* denotes the level of human effort expended.
**Economic Considerations:**
- The market price of fish per unit is $100.
- The constant marginal cost of effort is $50.
**Sustainable Harvest Equation:**
To maintain a sustainable level of harvesting, the equation in terms of population size \( S \) is:
\[ b_s = \text{(blank)} S(1 - S/\text{(blank)}) \]
The blank spaces would be filled with the appropriate values or expressions to complete the equation in educational content.
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