(Solution) - A population of bacteria has per capita production r -(2025 Original AI-Free Solution)

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A population of bacteria has per capita production r < 1, and 1.0 x 106 bacteria are added each generation. What happens to the equilibrium if r = 0? What happens if r is close to 1? Do these results make biological sense?
Find the equilibrium population of bacteria in the above case with supplementation.