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

MATH102 December 2013

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Question C 02 (a)

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: ${\frac {dF}{dt}}=I-\alpha NF$ Where I and $\alpha$ are constant and two cases for N are considered. Explain in words what the constant I represents.

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Hint
In the text, two actions are described that affect the amount of fish in the lake, one of which increases the amount of fish; the other decreases the amount of fish. Does the constant $I$ have a positive (increasing) or negative (decreasing) impact on the rate of change of fish in the lake? Does it depend on the current number of fish or fishermen?

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. The constant $I$ has a positive effect on the rate of change of the fish population (i.e., as $I$ increases, ${\tfrac {dF}{dt}}$ increases). It is also independent of the number of fish or fishermen. Hence, the constant $I$ represents the rate at which the company adds fish to the lake.