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Dr. Jordan studied a bat colony in a cave. He knew that $75$ of the bats in the cave had been tagged the week before. Then, he counted $480$ bats, of which $20$ were tagged. To the nearest whole number, what is the best estimate for the bat population?

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Estimate population size using proportions

Full solution

Q. Dr. Jordan studied a bat colony in a cave. He knew that

75

of the bats in the cave had been tagged the week before. Then, he counted

480

bats, of which

20

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

Set up proportion: Set up the proportion based on the data given. $\newline$ We know: $\newline$ - Tagged bats counted: $20$ $\newline$ - Total bats counted: $480$ $\newline$ - Total bats tagged previously: $75$ $\newline$ Let $N$ be the estimated total bat population. $\newline$ We set up the proportion as follows: $\newline$ $\frac{20}{480} = \frac{75}{N}$
Solve proportion: Solve the proportion by cross-multiplying to find $N$ . Cross-multiplying gives: $20 \times N = 75 \times 480$
Continue solving: Continue solving for $N$ . $20 \times N = 36000$ Divide both sides by $20$ to isolate $N$ : $N = \frac{36000}{20}$ $N = 1800$

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