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While doing research on a local river, a scientist put tags on $210$ rainbow trout. Later, the scientist captured $200$ rainbow trout, of which $12$ had tags. To the nearest whole number, what is the best estimate for the rainbow trout population?

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Estimate population size using proportions

Full solution

Q. While doing research on a local river, a scientist put tags on

210

rainbow trout. Later, the scientist captured

200

rainbow trout, of which

12

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

Set up proportion: Set up the proportion based on the tagging data. $\newline$ We know: $\newline$ - Marked trout in the second capture: $12$ $\newline$ - Total trout in the second capture: $200$ $\newline$ - Total trout marked initially: $210$ $\newline$ Let $N$ be the estimated total population of rainbow trout. $\newline$ The proportion is set up as: $\newline$ $\frac{12}{200} = \frac{210}{N}$
Solve for N: Solve the proportion for N. $\newline$ Cross-multiplying to solve for N: $\newline$ $12 \times N = 210 \times 200$ $\newline$ $12 \times N = 42000$
Isolate N: Divide both sides by $12$ to isolate N. $\newline$ $N = \frac{42000}{12}$ $\newline$ $N = 3500$

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