# Science:Math Exam Resources/Courses/MATH102/December 2013/Question C 02 (d)

MATH102 December 2013
Other MATH102 Exams

### Question C 02 (d)

The population of fish in a particular lake is given by the function F(t) where F is measured in number of fish and t is measured in days. A company that manages fish stocks is hired to restock the lake, adding fish at a constant rate. Only N fishers are allowed to fish in the lake at a time. A simple model for this scenario is given by the equation:

${\displaystyle {\frac {dF}{dt}}=I-\alpha NF}$

Where I and ${\displaystyle \alpha }$ are constant and two cases for N are considered.

Case 2: The agency that administers fishing permits decides that the number of fishers should be proportional to the number of fish currently in the lake, ${\displaystyle N=F/3}$. What is the population size ${\displaystyle F_{*}}$ to which F(t) approaches as ${\displaystyle t\to \infty }$ in this scenario?

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