Question

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?

Explanation:

Step1: Set up proportion

Let \( N \) be the total population. The proportion of tagged trout in the second capture should be approximately equal to the proportion of tagged trout in the entire population. So we have \(\frac{12}{200}=\frac{210}{N}\).

Step2: Solve for \( N \)

Cross - multiply: \( 12N = 200\times210 \). Then \( N=\frac{200\times210}{12} \). First, calculate \( 200\times210 = 42000 \). Then divide by 12: \( N=\frac{42000}{12}=3500 \).

Answer:

3500