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:
Where I and are constant and two cases for N are considered.
Explain in words what the constant I represents.
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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 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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The constant has a positive effect on the rate of change of the fish population (i.e., as increases, increases). It is also independent of the number of fish or fishermen.
Hence, the constant represents the rate at which the company adds fish to the lake.