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A group of volunteers tagged and released $34$ owls as part of a research project. Later, the researchers counted $300$ owls, $12$ of which had tags. To the nearest whole number, what is the best estimate for the owl population?

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Estimate population size using proportions

Full solution

Q. A group of volunteers tagged and released

34

owls as part of a research project. Later, the researchers counted

300

owls,

12

of which had tags. To the nearest whole number, what is the best estimate for the owl population?

Set up proportion: Step $1$ : Set up the proportion based on the information given. $\newline$ We know that $12$ out of $300$ owls were tagged, and originally $34$ owls were tagged and released. Let's denote the total owl population as $p$ . $\newline$ The proportion is set up as follows: $\newline$ $\frac{12}{300} = \frac{34}{p}$
Solve proportion: Step $2$ : Solve the proportion to find the estimated owl population. $\newline$ Cross-multiplying to solve for $p$ : $\newline$ $12 \times p = 34 \times 300$ $\newline$ $12 \times p = 10200$
Continue solving: Step $3$ : Continue solving for $p$ . $\newline$ Divide both sides by $12$ to isolate $p$ : $\newline$ $p = \frac{10200}{12}$ $\newline$ $p = 850$

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