(Solution) - Suppose that r 1 5 and h 1 0 -(2025 Original AI-Free Solution)

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Suppose that r = 1.5 and h = 1.0 × 106 bacteria.
A lab is growing and harvesting a culture of valuable bacteria described by the discrete-time dynamical system
bt + 1 = rbt - h.
The bacteria have per capita production r, and h are harvested each generation. Graph the updating function for each, and use the Slope Criterion for stability to check the stability.