top picture is the simple growth model, bottom picture is the realistic logistic model

Suppose fish grow in a lake owned by a fish company, and the company wants to harvest fish at a constant rate. The company knows how many fish are in the lake and how the population grows. The manager has a tough time determining the right number of fish to harvest. They hire you to help decide.

in the equations above Nt is the number of fish in the lake on the t'th day. r is the greatest possible per capita reproduction rate, and K is a constant. these models are for the fish population when the company catches no fish. what will happen if the company catches h fish per day? how large can h be without jeopardizing the population?

part 1: you first use the simple model to answer these questions. the company provides you with this data: current population is 200 thousand fish, and per capita reproduction rate is 1.01. Determine the following.

If the company captures the same number of fish, h, every day, what is the dynamical system for the fish population with harvest?

Are there any equilibria. Are they stable or unstable?

what's the highest fishing rate, h, that will not cause the fish to go extinct?

what will happen to the fish population if the company harvests at this rate?

Part 2: the company tells you that long ago when fishing in the lake had not begun, there were 300 thousand fish in the lake. you realize this is one of the equilibria for the logistic model that is above. with this additional information can you answer the same questions from part one using the logistic model?