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To monitor the buffalo population, scientists put a special mark on $25$ buffalo. Later, they flew over the area and kept track of the buffalo they saw. They counted a total of $920$ buffalo, $10$ of which were marked. To the nearest whole number, what is the best estimate for the buffalo population?

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Estimate population size using proportions

Full solution

Q. To monitor the buffalo population, scientists put a special mark on

25

buffalo. Later, they flew over the area and kept track of the buffalo they saw. They counted a total of

920

buffalo,

10

of which were marked. To the nearest whole number, what is the best estimate for the buffalo population?

Set up proportion: Set up the proportion based on the capture-recapture method. $\newline$ Marked buffalo seen: $10$ $\newline$ Total buffalo seen: $920$ $\newline$ Total buffalo marked: $25$ $\newline$ Let $p$ be the estimated buffalo population. $\newline$ Set up the proportion: $\newline$ $\frac{10}{920} = \frac{25}{p}$
Solve proportion: Solve the proportion by cross-multiplying to find $p$ . $10 \times p = 25 \times 920$
Continue solving: Continue solving for $p$ . $10 \times p = 23000$ $p = \frac{23000}{10}$ $p = 2300$

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