Question
In: Math
The initial mass of a certain species of fish is 7 million tons. The mass of...
The initial mass of a certain species of fish is 7 million tons. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of 2/yr initially, but over time if the population gets too high it would reach a maximum sustainable population of 50 million tons.
1. Suppose, commercial fishing removes fish mass at a constant rate of 15 million tons per year. Set up the initial value problem which determines the fish mass, F(t), in millions of tons at time t in years.
2. For your harvesting model above, what will the long term behavior of the fish population be?
Solutions
milcah answered 2 years agoRelated Solutions
Suppose that fishing has caused a certain species of fish to be threatened with extinction. After...
Suppose that fishing has caused a certain species of
fish to be threatened with extinction. After banning fishing for
many years, the fish population has rebounded. Now the government
is proposing to introduce a system of tradeable fishing permits,
which entitles the holder of each permit to catch a given number of
fish each year. Explain how uncontrolled fishing led to a negative
externality problem and how a system of tradeable fishing permits
can potentially overcome the inefficiency caused by...
You are a researcher studying a certain species of fish in a local lake. You gather...
You are a researcher studying a certain species of fish in a
local lake. You gather a random sample of 18 fish of this species
and record the lengths (in centimeters) of the fish. The data is
displayed in the table below. Estimate the mean length of all fish
of this type in the lake. Use a 98% confidence level. 10.8 9.4 7.7
10.9 6.8 8.9 8.3 8.5 8.4 8 11.3 7.9 8.6 8.5 11.1 11.3 8.1 6.9
(Checksum: 161.4)...
Certain species of blind fish living in perpetual darkness in the ocean depths have evolved from...
Certain species of blind fish living in perpetual darkness in
the ocean depths have evolved from ancestors that could see.
Research indicates that the brain centers for vision in these fish
is degenerating, whereas the brain centers controlling other senses
are enlarging. What might be the MOST probable reason for the loss
of vision in these fish?
A. exposure to mutagens that caused the loss of vision
B. progressive selection of genetic variants in the population
leading to blindness as...
The length of a species of fish is to be represented as a function of the...
The length of a species of fish is to be represented as a
function of the age (measured in days) and water temperature
(degrees Celsius). The fish are kept in tanks at 25, 27, 29 and 31
degrees Celsius. After birth, a test specimen is chosen at random
every 14 days and its length measured.
Age
Temp
Length
1
14
25
620
2
28
25
1,315
3
41
25
2,120
4
55
25
2,600
5
69
25
3,110
6
83...
The length of a species of fish is to be represented as a function of the...
The length of a species of fish is to be represented as a
function of the age (measured in days) and water temperature
(degrees Celsius). The fish are kept in tanks at 25, 27, 29 and 31
degrees Celsius. After birth, a test specimen is chosen at random
every 14 days and its length measured.
Age
Temp
Length
1
14
25
620
2
28
25
1,315
3
41
25
2,120
4
55
25
2,600
5
69
25
3,110
6
83...
Malaysia can produce 20 tons of fish or 5 tons of rice per month. Thailand can...
Malaysia can produce 20 tons of fish or 5 tons of rice per
month. Thailand can produce 25 tons of fish or 20 tons of rice per
month.
a) Assuming both countries are using the same amount of capital
and labor, which country has the absolute advantage in producing
fish? In producing rice?
b) What is the opportunity cost of producing one ton of fish for
Malaysia? For Thailand? Show work.
c) What is the opportunity cost of producing one...
The Blue Wild Fish Company sells a particular species of fish that live in a local...
The Blue Wild Fish Company sells a particular species of fish
that live in a local lake. In the entire lake the distribution of
fish lengths follows a normal distribution with mean 26 inches and
standard deviation 7.8 inches.
You have 5 attempts for numeric answers and 1 attempt for multiple
choice answers. Round answers to 2 decimal places.
1. A fisherman goes out and catches 45 fish every day. If we were
to look at the distribution of the...
REGRESSION. The length of a species of fish is to be represented as a function of...
REGRESSION. The length of a species of fish is to be represented
as a function of the age (measured in days) and water temperature
(degrees Celsius). The fish are kept in tanks at 25, 27, 29 and 31
degrees Celsius. After birth, a test specimen is chosen at random
every 14 days and its length measured. The dataset is presented
below. What is the estimated regression equation?
Age
Temp
Length
1
14
25
620
2
28
25
1,315
3
41...
In a certain population of fish, the lengths of the individual fish follow approximately a normal...
In a certain population of fish, the lengths of the individual
fish follow approximately a normal distribu- tion with mean 54.0 mm
and standard deviation 4.5 mm. We saw in Example 4.3.1 that in this
situation 65.68% of the fish are between 51 and 60 mm long. Suppose
a ran- dom sample of four fish is chosen from the population. Find
the probability that
(a) allfourfisharebetween51and60mmlong.
(b) the mean length of the four fish is between 51 and 60
mm....
In a certain scattering experiment, protons with mass m are fired with initial kinetic energy K0...
In a certain scattering experiment, protons with mass m are
fired with initial kinetic energy K0 (momentum p0) at a target
consisting of helium atoms (the mass of a helium atom is
approximately 4m). Protons scattered at an angle of 90◦ relative to
their initial direction of motion are measured to have a kinetic
energy of Kp = 0.54K0 (corresponding to a momentum of pp). Assuming
that each outgoing proton collided with one and only one helium
atom, is this...
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