Question

anna, a graduate student, needed to estimate how many catfish were in a local river. first, she marked 360 catfish with tags. later, she captured 650 catfish, of which 30 had tags. to the nearest whole number, what is the best estimate for the catfish population?

Explanation:

Step1: Set up proportion

Let \( N \) be the total population. The proportion of tagged fish in the second capture should be equal to the proportion of tagged fish in the total population. So \(\frac{30}{650}=\frac{360}{N}\)

Step2: Solve for \( N \)

Cross - multiply: \( 30N = 360\times650 \)
First, calculate \( 360\times650=234000 \)
Then, \( N=\frac{234000}{30} \)

Step3: Calculate \( N \)

\( N = 7800 \)

Answer:

7800