9 in a fish farm a population of fish is introduced

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) equation
dP
dt
= r
0
1 -
P ( t )
P
c
P ( t ) - βP ( t )
where r
0
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.
1. What value of dP/dt corresponds 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 if β is raised to 5%?
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