9 in a fish farm a population of fish is introduced

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9. (****) In a fish farm, a population of fish is introduced into a pond and harvested regularly.A model for the rate of change of fish population is given by the (differential) equationdPdt=r01-P(t)PcP(t)-βP(t)wherer0is the birth rate of the fish,Pcis the maximum population that the pond cansustain (called thecarrying capacity), andβis the percentage of the population that isharvested.1. What value ofdP/dtcorresponds to a stable population?
2. If the pond can sustain 10,000 fish, the birth rate is 5%, and the harvesting rate is 4%,find the stable population level.
3. What happened ifβis raised to 5%?5
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Chapter 2 / Exercise 13
Essential Calculus
Stewart
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Term
Spring
Professor
LAMB
Tags
Math, Derivative, Differential Calculus, lim, Natural logarithm, Logarithm
We have textbook solutions for you!
The document you are viewing contains questions related to this textbook.
Essential Calculus
The document you are viewing contains questions related to this textbook.
Chapter 2 / Exercise 13
Essential Calculus
Stewart
Expert Verified

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