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Scientists tagged $770$ pike for a research project about a local lake. Later, they trapped $270$ pike, of which $21$ had tags. To the nearest whole number, what is the best estimate for the pike population?

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Estimate population size using proportions

Full solution

Q. Scientists tagged

770

pike for a research project about a local lake. Later, they trapped

270

pike, of which

21

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

Set up proportion: Set up the proportion based on the capture-recapture method used in the problem. We know: $\newline$ - Tagged pikes initially: $770$ $\newline$ - Total pikes caught in the second round: $270$ $\newline$ - Tagged pikes found in the second round: $21$ $\newline$ We set up the proportion as follows: $\newline$ $\frac{21}{270} = \frac{770}{p}$ , where $p$ is the estimated total pike population.
Cross multiply: Cross multiply to solve for $p$ : $21 \times p = 770 \times 270$ .
Solve for p: Solve for p: $\newline$ $21 \times p = 207900$ , $\newline$ $p = \frac{207900}{21}$ , $\newline$ $p = 9900$ .

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