Question

.
In City Lake, researchers caught, marked, and released 213 bass. Later, they took a sample of 104 bass and found that 13 were marked.
Which proportion can you solve to estimate the number of bass in the lake?

Answer 1

To estimate the number of bass in the lake, you can set up a proportion based on the information you've provided.

Let \( N \) be the total number of bass in the lake.

From the information given:

- The number of bass that were initially marked and released: 213
- The number of bass in the sample: 104
- The number of marked bass found in the sample: 13

You can set up the proportion as follows:

\[
\frac{\text{Number of marked bass in the sample}}{\text{Total number of bass in the sample}} = \frac{\text{Total number of marked bass}}{\text{Total number of bass in the lake}}
\]

Substituting in the numbers:

\[
\frac{13}{104} = \frac{213}{N}
\]

This proportion can be solved to estimate \( N \), the total number of bass in the lake. Cross-multiplying gives you:

\[
13N = 213 \times 104
\]

Now you can solve for \( N \). First, calculate \( 213 \times 104 \):

\[
213 \times 104 = 22152
\]

Now, divide both sides by 13 to find \( N \):

\[
N = \frac{22152}{13} \approx 1704
\]

So, the estimated number of bass in the lake is approximately 1704.