Let P(t) represent the population of a non-native species introduced to a new area for the purposes of harvesting. Suppose we intially introduce P0 = 100 indicidcuals and suppose the population grows exponentially with growth-rate coefficient k=2 if there is no harvesting (for example, suppose that there are no predators in the area, and there are ample resources). HOw should we manage the harvesting of the new species? in other words, how should we set the harvesting rate C in the model

Question

Let P(t) represent the population of a non-native species introduced to a new area for the purposes of harvesting.  Suppose we intially introduce P0 = 100 indicidcuals and suppose the population grows exponentially with growth-rate coefficient k=2 if there is no harvesting (for example, suppose that there are no predators in the area, and there are ample resources).  HOw should we manage the harvesting of the new species? in other words, how should we set the harvesting rate C in the model

dP/dt = k*P - C,

so that the population remains steady at P = 100,000 individuals?  Can we use a particular harvesting rate forever, or will the rate have to be adjusted?  How closely will we need to monitor the population?