   Chapter 2.7, Problem 36E

Chapter
Section
Textbook Problem

# In a fish farm, a population of fish is introduced into a pond and harvested regularly. A model for the rate of change of the fish population is given by the equation d P d t = r 0 ( 1 − P ( t ) P c ) P ( t ) − β+ P ( t ) where r0 is the birth rate of the fish, P c , is the maximum population that the pond can sustain (called the carrying capacity), and β is the percentage of the population that is harvested.(a) What value of dP/dt corresponds to a stable population?(b) If the pond can sustain 10, 000 fish, the birth rate is 5%, and the harvesting rate is 4%, find the stable population level.(c) What happens if β is raised to 5%?

To determine

Part (a)

To find:

The value of dPdt corresponds to a stable population

Explanation

1) Given:

dPdt=r01- PtPcPt-ΒP(t)

2) Calculation:

Stable population means the population is not changing

Therefore,

For the stable population dPdt=0

dPdt=r01- PtPcP

To determine

Part (b)

To find:

The stable population level

To determine

Part (c)

To find:

What happens when Β is raised to 5%

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