Ononot — A bacterial population follows the model Pn = 0.75P{n-1} + 8

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Recurrence Relationshard

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A bacterial population follows the model $P_n = 0.75P_{n-1} + 800,$ where $P_n$ is the population at generation $n$ .

What is the long-term equilibrium population (the value $L$ toward which $P_n$ converges)?