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A researcher who was conducting a study caught, tagged, and released $95$ opossums. Weeks later, the researcher caught a total of $170$ opossums, of which $19$ were tagged. To the nearest whole number, what is the best estimate for the opossum population?

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Estimate population size using proportions

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Q. A researcher who was conducting a study caught, tagged, and released

95

opossums. Weeks later, the researcher caught a total of

170

opossums, of which

19

were tagged. To the nearest whole number, what is the best estimate for the opossum population?

Set up proportion: Step $1$ : Set up the proportion based on the capture-recapture method. $\newline$ We know: $\newline$ - Tagged opossums found: $19$ $\newline$ - Total opossums caught in second round: $170$ $\newline$ - Total opossums tagged initially: $95$ $\newline$ Let $N$ be the estimated opossum population. $\newline$ The proportion is set as: $\newline$ $\frac{19}{170} = \frac{95}{N}$
Solve for N: Step $2$ : Solve for N by cross-multiplying. $\newline$ Cross-multiplying gives: $\newline$ $19 \times N = 95 \times 170$
Continue solving for N: Step $3$ : Continue solving for N. $\newline$ $19 \times N = 16150$ $\newline$ $N = \frac{16150}{19}$ $\newline$ $N = 850$

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