Sea lice are a parasite that feed on salmon. They occur naturally in low densities on wild salmon, but crowded conditions on salmon farms are ideal for sea louse outbreaks. Sea lice from salmon farms can spread onto wild migrating salmon. To help protect wild salmon, the Canadian federal government requires salmon farms to treat their sh with a parasiticide (or else to harvest the sh) when sea lice counts on a salmon farm reach a threshold of three motile lice per sh. A model for sea louse population on a salmon farm before and after treatment is given by (t)- Peat ift 0 are constant parameters. 3. (a) Use the limit definition of derivative to show that p(t) satisfies the differential equation p' (t) = Jap(t) ift T' (You may use without proof the fact that lim ch - 1 h -+0 h = log(c) for all c > 0.) (b) Which of the two farms, Sargeaunt Pass or Humphrey Rock, has a larger parameter a? Justify your answer carefully.6 - 4 2 0 - Nov Jan Mar May Jul Motile louse abundance (ind. fish-1) 876 6 4 2 Nov Jan Mar May Month 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