Suppose you're tasked to program a realistic model for the population of Wharf Roaches on someone's...

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Suppose you're tasked to program a realistic model for the population of Wharf Roaches on someone's Animal Crossing island. This island is designed to have a carrying capacity of 360 Wharf Roaches, and a growth rate of 10%. It is also assumed a player will capture f = 5 Wharf Roaches a day to be sold for bells (the island unit of currency). The ODE that describes their population is given by: P' = rP|1- (-) - What is the least number of Wharf Roaches you can start with so the population won't go extinct? In other words, what is the minimal initial population (Po) the island can start with so the Wharf Roach population doesn't go exinct? I caught a wharf roach! This water-loving roach has no pier! (Img source: Animal Crossing Wiki) Suppose you're tasked to program a realistic model for the population of Wharf Roaches on someone's Animal Crossing island. This island is designed to have a carrying capacity of 360 Wharf Roaches, and a growth rate of 10%. It is also assumed a player will capture f = 5 Wharf Roaches a day to be sold for bells (the island unit of currency). The ODE that describes their population is given by: P' = rP|1- (-) - What is the least number of Wharf Roaches you can start with so the population won't go extinct? In other words, what is the minimal initial population (Po) the island can start with so the Wharf Roach population doesn't go exinct? I caught a wharf roach! This water-loving roach has no pier! (Img source: Animal Crossing Wiki)