To track the reptile population around a lake, researchers marked 200 turtles. A few weeks later, they counted 480 turtles, of which 64 were marked. To the nearest whole number, what is the best estimate for the turtle population?




This problem involves using the **capture-recapture method** for estimating a population. Here's how we can set it up:

Let \( P \) represent the total turtle population. The proportion of marked turtles in the entire population should be the same as the proportion of marked turtles in the second sample. We can set up the proportion like this:

\[
\frac{200}{P} = \frac{64}{480}
\]

### Solving for \( P \):

1. Cross-multiply:

\[
200 \times 480 = 64 \times P
\]

\[
96000 = 64P
\]

2. Solve for \( P \):

\[
P = \frac{96000}{64} = 1500
\]

So, the best estimate for the total turtle population is **1,500**.

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Would you like further details on this solution? Here are some related questions to think about:

1. What assumptions are made when using the capture-recapture method?
2. How would the estimate change if the number of marked turtles in the second sample was lower?
3. Can this method be used for estimating populations of other animals? Why or why not?
4. What factors could introduce error into the estimate provided by this method?
5. How could the researchers improve the accuracy of their estimate?

**Tip:** In population estimation, it's crucial that marked individuals have an equal chance of being captured again to avoid bias.

To track the reptile population around a lake, researchers marked 200 turtles. A few weeks later, they counted 480 turtles, of which 64 were marked. To the nearest whole number, what is the best estimate for the turtle population?

Learn how to estimate the turtle population around a lake using the capture-recapture method. The problem involves proportion and population estimation concepts, with a detailed step-by-step solution. Suitable for students in Grades 9-11.

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