Question

scientists captured, tagged, and released 47 ducks as part of a research study. a week later, the scientists returned to the area and found 23 tagged ducks out of the 230 ducks they counted. to the nearest whole number, what is the best estimate for the duck population?

Explanation:

Step1: Set up proportion

Let \( x \) be the duck population. The proportion of tagged ducks in the first sample (47 tagged out of \( x \) total) should equal the proportion of tagged ducks in the second sample (23 tagged out of 230 total). So, \(\frac{47}{x}=\frac{23}{230}\).

Step2: Solve for \( x \)

Cross - multiply: \( 23x = 47\times230 \).
First, calculate \( 47\times230=47\times200 + 47\times30=9400+1410 = 10810 \).
Then, \( x=\frac{10810}{23}\).
Calculate \( \frac{10810}{23}=470 \).

Answer:

470