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TT

Tamara T.

Differential Equations

3 hours ago

Find the general solution

MS

Merve S.

Differential Equations

8 hours ago

Could you solve it?

MS

Merve S.

Differential Equations

8 hours ago

Could you solve it?

MS

Merve S.

Differential Equations

11 hours ago

Could you solve it?

MS

Merve S.

Differential Equations

11 hours ago

Could you solve it?

MS

Merve S.

Differential Equations

11 hours ago

Could you solve it?

MS

Merve S.

Differential Equations

14 hours ago

Could you solve it?

MS

Merve S.

Differential Equations

14 hours ago

Could you solve it?

MS

Merve S.

Differential Equations

14 hours ago

Could you solve it?

MS

Merve S.

Differential Equations

14 hours ago

Could you solve it?

MS

Merve S.

Differential Equations

14 hours ago

Could you solve it ?

MT

Markus T.

Differential Equations

1 day, 3 hours ago

Analyze the scalability of the following model: dS/dt = -BetaSI - gamma(R) dI/dt = BetaSI - alpha(I) dR/dt = alpha(I) - gamma(R)

MS

Merve S.

Differential Equations

1 day, 10 hours ago

Could you solve it?

MS

Merve S.

Differential Equations

1 day, 10 hours ago

Could you solve it?

MS

Merve S.

Differential Equations

1 day, 11 hours ago

Could you solve it?

MS

Merve S.

Differential Equations

1 day, 11 hours ago

Could you solve it?

kh

Kelvin H.

Differential Equations

1 day, 23 hours ago

In this project, you will study various models of a fishery including effects from fishing by humans. Let P(n) represent the total mass of mature Pacific halibut in units of 106 kg. We will model the wild halibut biomass without any fishing by the following logistic difference equation: P(n+1)=(1.71) P(n) - (0.00875) (P(n+1))2 Here, r=0.71 and r/M=0.00875 (A) (i) (C)Suppose the halibut stock started out at 95% of the carrying capacity according to the model above. But in one massive fishing effort, the halibut biomass is reduced all the way down to 1,000,000 kg (say all within one year). If no further fishing is allowed until stocks recover to 95% of the carrying capacity, how long will that take according to the model? Estimate (to the nearest year) by creating a series of P(n) for years n=1,2,3,... and see which year exceeds 95% of M. According to the table, the fish stock would only exceed 95 percent of the carrying capacity during the first year. (ii) (A) What would be the average fish amount taken per year if this process of massive to 1,000,000 kg in one year followed by no fishing until the population recovered to 95% carrying capacity was done repeatedly over a long period? The average fish amount taken per year through this process would be around 15,000kg for the first year, but gradually decreasing to 500 kg for the second year, following to 15 kg in the third year, etc. Based on the data calculated, it has shown a decreasing trend that fishes would maintain a steady population if human activities were not directly interfering. (B) One way to make use of a resource like the halibut fishery that is less drastic than the approach in (A) is to take some constant amount of the fish biomass every year for human use. (i) (As) Suppose that everything remains as in the equation above, but some constant amount h (in 106 kg) of halibut biomass is removed each year via fishing. What modified difference equation models this situation? (Think about the derivation of (7.8 from MDA) and take the fishing amount h into account.) P (n + 1) = (1 + r) P(n) ÔÇô r (P(n)) ^2/ M When a constant amount of halibut biomass is removed throughout the population via fishing, the population biomass would decrease when thinking without analysis and application of the first hand. If the constant number of fishes are taken out too much, it creates an imbalance that can erode the food web and lead to a loss of other important marine life, including vulnerable species like sea turtles and corals. When there is less fish in the fishery, fishes that did not reach the best age to harvest would be fished beforehand, which Reductions in age and size at maturity may affect recovery negatively (Hutchings 2002, Roff 2002). Earlier maturity can be associated with reduced longevity, increased post reproductive mortality, and smaller sizes at reproductive age. (ii) (Co) Investigate the solutions of your constant harvesting difference equation from part (i) if the fishing term is each of these values: h = 5, 10, 14, 20, one at a time. Choose enough different P(0) values for each so that you think you see the whole picture and then describe what is happening in words. In particular, for each h, how many different equilibrium solutions are there? Where are they located? How do they change as increases? Are they stable or unstable? (iii) (R) The situation here is often described by saying that a harvesting level h > 0 introduces a threshold value for the population. If P(0) is greater than the threshold, the population increases to a positive equilibrium, but if P(0) is less than the threshold, the population crashes. What are the threshold values for the h that you considered in part (ii)? (iv) (C) By rewriting your difference equation from part (i) in the form P(n+1) - P(n) = ..., what is the maximum value of h for which the equation still has a stable equilibrium? (Hint: This question can be answered by means of algebra alone if you think about it the right way - but answer however you wish). (v) (I) What should it mean to say that a fishing level h is sustainable? What is the maximum sustainable constant fishing level? Does the answer depend on what the initial value P(0) at the start of the fishing intervention is? (vi) (A) What would be the average fish amount taken per year if constant harvesting at the maximum sustainable level is done repeatedly over a long period? (C) Instead of taking a constant amount of fish, we could also take a constant proportion of whatever fish biomass is present (i) (As) Next, suppose that everything remains as in the equation at the top, but instead of a constant amount, suppose that a constant proportion p of the halibut biomass (whatever it is) is removed each year via fishing. What modified difference equation models this situation? (Think about the derivation of (7.8) in MDA and take the proportion removed by fishing into account). (ii) (Co) Investigate the solutions of your constant harvesting differential equation from part (i) if the fishing term is each of these values: p = 0.1, 0.3, 0.5, 0.8, one at a time. Choose enough different P(0) values so that you think you see the whole picture and then describe what is happening in words. In particular, for each value of p how many different equilibrium solutions are there? Where are they located? How do they change as p increases? Are they stable or unstable? (iii) (C) By rewriting your difference equation from part (i) in the form P(n+1) - P(n) = ..., what is the p for which the halibut population starts to "crash" for all P(0)? (This question can be answered by means of algebra alone if you think about it the right way. And the answer should make biological sense too!) (iv) (I) What should it mean to say that a fishing proportion p is sustainable? What values of p are sustainable? Does the answer depend on what the initial value P(0) at the start of the fishing intervention is? (v) (A) What would be the average fish amount taken per year if proportional harvesting at the level p = 0.3 is done repeatedly over a long period? (D) (Co) Compare the strategies in parts (A), (B), and (C) from the point of view of their effect on the halibut fishery and the average amounts taken per year. If you were going to recommend one, which would it be? Explain how you made your determination. (E) (Co) Which strategy would the fishing community want and why?

MA

M A.

Differential Equations

2 days ago

Variable separable

ap

Anonymous P.

Differential Equations

2 days, 3 hours ago

The population of fish in a lake grows logistically according to the differential equation where t is in years with no harvesting. If the lake has 550 fish and opens to fishing, determine how many fish can be harvested pur year to maintain equilibrium. \frac{dy}{dt}=.1y(1-\frac{y}{2500})

ap

Anonymous P.

Differential Equations

2 days, 5 hours ago

Let y' = sin(xy) and y(0) = 1 Approximate y(5) using Eulers method with a step size of .5

CB

Catherine B.

Differential Equations

2 days, 6 hours ago

Fifteen cases of measles have been reported from an inner city area, the ?rst for several years. All are children aged 8 to 15 years who had previously received one measles vaccination as infants. Thiswas the recognised policy at the time but it is not known if it conferred complete and lifelongimmunity. The problem is to decide whether to recommend that all children in this age group whowere vaccinated once only be revaccinated.In the context of an inner city epidemic the Center for Disease Controls estimates that 20 out of every 100 children aged 8 to 15 will come in contact with an infectious case of measles each year.Evidence from the literature gives the probability of getting measles if exposed to aninfectious case is 0.33 in a child who received only one measles vaccination and 0.05if revaccinated. During the current epidemic the probability of dying from measles if a child is 23 per 10 000 cases (0.0023).Calculate the number of preventable deaths from measles if a strategy of revaccination is adopted?If the cost of revaccination is £3.00 per child what is the cost per life saved for every 100,000children? How would these ?gures change given that the probability of exposure to an infectiouscase of measles varies from 1 in a 100 in a rural area to 45 per 100 in a city ward? Discuss yourresults

KS

Kristina S.

Differential Equations

None

What is the balanced equation for C4H10+O2+3.756N2 CO2+H2O+N2

MA

M A.

Differential Equations

2 days, 12 hours ago

Variable Separable

MA

M A.

Differential Equations

2 days, 12 hours ago

Variable Separable

MA

M A.

Differential Equations

2 days, 12 hours ago

Variable Separable

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