Question

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 \begin{equation} p(t) = \begin{cases} Pe^{at} & \text{if } t < T \\ Qe^{-dt} & \text{if } t \ge T \end{cases} \end{equation} 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.)

          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
\begin{equation*}
p(t) = \begin{cases} Pe^{at} & \text{if } t < T \\ Qe^{-dt} & \text{if } t \ge T \end{cases}
\end{equation*}
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.)

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) = Pe^at if t < T
Qe^-dt 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.)

Added by John B.

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