The population of fish in a fishery has a growth rate that is proportional to its size when the population is small. However, the fishery has a fixed capacity and the growth rate will be negative if the population exceeds that capacity.

The population of fish in a fishery has a growth rate that is proportional to its size when the population is small. However, the fishery has a fixed capacity and the growth rate will be negative if the population exceeds that capacity.

A. Formulate a differential equation for the population of fish described in the scenario, defining all parameters and variables.

1. Explain why the differential equation models both conditions in the scenario.

B. Adjust the differential equation from part A to account for the following modification: the fish are continually harvested at a rate proportional to the square root of the number of fish in the fishery.

1. Explain why the adjustment to the differential equation models the modification to the scenario.

 

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