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# Production Equation

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Age 16 to 18

Challenge Level

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Taking $X_n$ as the amount of stock at the end of week $n$, you
need to solve the difference equation (recurrence relation)
$$X_{n+1} = X + (1 - {p\over 100})X_n$$ Put $X_n = Y_n - C$ then
choose $C$ such that $$Y_{n+1} = (1 - {p\over 100})Y_n$$ and
consider the values of this expression for $Y_n, Y_{n-1}, Y_{n-2},
... Y_1, Y_0$.