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To estimate the number of moths in a certain region, Wanda traps $77$ moths and marks them. She releases these moths and then later catches $320$ , $28$ of which are marked. To the nearest whole number, what is the best estimate for the moth population?

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Estimate population size using proportions

Full solution

Q. To estimate the number of moths in a certain region, Wanda traps

77

moths and marks them. She releases these moths and then later catches

320

,

28

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

Set up proportion: Step $1$ : Set up the proportion based on the capture-recapture method.
Solve proportion: Step $2$ : Solve the proportion by cross-multiplying to find $M$ .
Isolate and solve: Step $3$ : Divide both sides by $28$ to isolate $M$ and solve for the estimated population.

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