After treatment on a salmon farm, the population of sea lice follows the differential equation P3(t)'=-dp3(t)...

  

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After treatment on a salmon farm, the population of sea lice follows the differential equation P3(t)'=-dp3(t) which has the solution pз(t) = Qed where Q and d are positive constants. Using this information, which of the two farms in Figure 2, Sargeaunt Pass or Humphrey Rock has a larger parameter d? Justify your answer carefully. 4. (★★✰✰) Now let's put everything together to find out when a salmon farm should treat their fish. If we assume that the sea louse population is mainly driven by sea lice reproducing within the farm, then a model for the sea louse population before and after treatment is p(t) = . [Peat if t<T -dt Qe if t≥ T where p(t) is the number of motile lice per fish at time t in days, T is the time of treatment, and P,Q, a, d> 0 are constant parameters. (a) Find the value of Q such that p(t) is continuous for all t. (b) On the Sargeaunt Pass farm, the parameter a was measured to have the value a = 0.048 and the parameter d was measured to have the value d = 0.057. Juvenile wild salmon begin migrating past the farm on March 1. If the sea louse population on January 1st is 0.5 motile lice per fish what is the latest date treatment should occur to ensure that the sea lice population on the farm is less than 3 motile lice per fish by the time of wild salmon migration? (Assume it is not a leap year and assume p(t) is a continuous function.) Motile louse abundance (ind. fish-1) 2. 6- a Nov Jan σ Mar May Νον Jan Mar May Month انال انال Figure 2: Number of motile sea lice per fish during the winter of 2005-2006 on two salmon farms in the Broughton Archipelago: (a) Sargeaunt Pass and (b) Humphrey Rock. The dashed line indicates the time of parasiticide treatment and the solid line is the best fit line to the data. Before treatment the best fit line is whichever function, p,(t) or p2(t), best describes the data (where p; (t) needs to be of the form Pe" and p2(t) needs to be of the form (1-e)). After treatment the best fit line is the function p,(t), where the parameters Q and d have been chosen so pa(t) fits the data the best. After treatment on a salmon farm, the population of sea lice follows the differential equation P3(t)'=-dp3(t) which has the solution pз(t) = Qed where Q and d are positive constants. Using this information, which of the two farms in Figure 2, Sargeaunt Pass or Humphrey Rock has a larger parameter d? Justify your answer carefully. 4. (★★✰✰) Now let's put everything together to find out when a salmon farm should treat their fish. If we assume that the sea louse population is mainly driven by sea lice reproducing within the farm, then a model for the sea louse population before and after treatment is p(t) = . [Peat if t<T -dt Qe if t≥ T where p(t) is the number of motile lice per fish at time t in days, T is the time of treatment, and P,Q, a, d> 0 are constant parameters. (a) Find the value of Q such that p(t) is continuous for all t. (b) On the Sargeaunt Pass farm, the parameter a was measured to have the value a = 0.048 and the parameter d was measured to have the value d = 0.057. Juvenile wild salmon begin migrating past the farm on March 1. If the sea louse population on January 1st is 0.5 motile lice per fish what is the latest date treatment should occur to ensure that the sea lice population on the farm is less than 3 motile lice per fish by the time of wild salmon migration? (Assume it is not a leap year and assume p(t) is a continuous function.) Motile louse abundance (ind. fish-1) 2. 6- a Nov Jan σ Mar May Νον Jan Mar May Month انال انال Figure 2: Number of motile sea lice per fish during the winter of 2005-2006 on two salmon farms in the Broughton Archipelago: (a) Sargeaunt Pass and (b) Humphrey Rock. The dashed line indicates the time of parasiticide treatment and the solid line is the best fit line to the data. Before treatment the best fit line is whichever function, p,(t) or p2(t), best describes the data (where p; (t) needs to be of the form Pe" and p2(t) needs to be of the form (1-e)). After treatment the best fit line is the function p,(t), where the parameters Q and d have been chosen so pa(t) fits the data the best.

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Based on the information given Before treatment both farms sea lice populations follow the equation ... View the full answer