A lake with a fixed carrying capacity contains a certain fish population. The fish population in the lake has a growth rate that is proportional to its size when the population is very small relative to the carrying capacity. However, when the fish population exceeds the carrying capacity, the growth rate is negative.

A. What is a differential equation that models the population of fish described in the Scenario section, defining all parameters and variables?

1. Explain how the differential equation models both conditions in the Scenario section.

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

1. Explain why the adjustment to the differential equation from part B models the modification to the Scenario section.