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Jerry studies bottlenose dolphins and wants to estimate the population in a certain region. Jerry catches $170$ dolphins, marks them, and releases them. Later on, Jerry catches $240$ dolphins and observes that $12$ of them are marked. To the nearest whole number, what is the best estimate for the dolphin population?

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Estimate population size using proportions

Full solution

Q. Jerry studies bottlenose dolphins and wants to estimate the population in a certain region. Jerry catches

170

dolphins, marks them, and releases them. Later on, Jerry catches

240

dolphins and observes that

12

of them are marked. To the nearest whole number, what is the best estimate for the dolphin population?

Set up proportion: Set up the proportion based on the capture-recapture method. $\newline$ Marked dolphins found: $12$ $\newline$ Total dolphins in second capture: $240$ $\newline$ Total dolphins marked initially: $170$ $\newline$ Let $N$ be the estimated dolphin population. $\newline$ The proportion is set as: $\newline$ $\frac{12}{240} = \frac{170}{N}$
Solve proportion: Solve the proportion by cross-multiplying to find $N$ . $12 \times N = 170 \times 240$
Continue solving: Continue solving for $N$ . $12 \times N = 40800$ $N = \frac{40800}{12}$ $N = 3400$

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