Many bird species on the Pitcairn Islands are in decline. In order to estimate the population of a particular species of bird, scientists mark 23 birds by attaching very small computer chips to them. A few days later, the scientists catch 240 birds, 12 of which are marked with computer chips. To the nearest whole number, what is the best estimate for the bird population?

We can again use the **mark and recapture** method to estimate the bird population.

Let's define the variables:
- \( N \) = total bird population (what we want to find)
- \( M \) = number of birds originally marked (23 birds)
- \( C \) = total number of birds caught in the second sample (240 birds)
- \( R \) = number of marked birds in the second sample (12 birds)

According to the mark and recapture method, the following proportion holds:

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

Substituting the values:

\[
\frac{12}{240} = \frac{23}{N}
\]

To find \( N \), solve the equation:

\[
N = \frac{23 \times 240}{12}
\]

Now, let's calculate it:

\[
N = \frac{5520}{12} = 460
\]

So, the best estimate for the bird population on the Pitcairn Islands is **460**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What could cause a marked bird to be less likely to be recaptured?
2. How does the length of time between capturing and recapturing affect the estimate?
3. What are some alternative methods for estimating animal populations?
4. How would the estimate change if more birds were captured in the second sample?
5. What are the limitations of using the mark and recapture method for bird populations?

**Tip:** When estimating wildlife populations, consider environmental factors that might affect the likelihood of recapture, such as changes in weather or migration patterns.

Learn how to estimate bird populations using the mark and recapture method. Solve a problem involving marking birds with computer chips and recapturing them to determine population size. Suitable for Grades 9-12.

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