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