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I have made the following time series formulation: $$Y_t = (1-K/X)Y_t-1 + PK$$

where $K \leq X$ and $0 \leq P \leq1$.

I'm looking to turn this into a formula to calculate the time period $t$ by only inputting $Y_t$, $K$, $X$ and $P$ as variables.

I can generate a table and plot of $Y_t$ vs $t$ and read from a spreadsheet table.

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