A group of researchers wanted to monitor the trout population, so they marked 340 trout with tags. Later, they captured 600 trout and found that 30 of them had tags. What is the BEST estimate for the trout population?

Question

Responses
A 6,2006,200
B 6,4006,400
C 6,6006,600
D 6,8006,800

Answer 1

To estimate the total trout population, we can use the capture-recapture method. The formula for this method is:

\[ \frac{\text{Number of marked trout}}{\text{Total trout population}} = \frac{\text{Number of marked trout recaptured}}{\text{Total trout captured}} \]

Let's denote:

• \( M = 340 \) (the number of marked trout),
• \( N = ? \) (the total trout population),
• \( m = 30 \) (the number of marked trout recaptured),
• \( C = 600 \) (the total number of trout captured).

Using the formula, we have:

\[ \frac{M}{N} = \frac{m}{C} \]

Substituting the known values:

\[ \frac{340}{N} = \frac{30}{600} \]

Now, we simplify the fraction on the right side:

\[ \frac{30}{600} = \frac{1}{20} \]

So now we have:

\[ \frac{340}{N} = \frac{1}{20} \]

Cross-multiplying gives:

\[ 340 \times 20 = N \]

Calculating the left side:

\[ 6800 = N \]

Thus, the best estimate for the trout population is:

D. 6,800