A country in Africa is trying to restore its giraffe population and is carefully keeping track of how many giraffes are in the area. To do so, local wildlife authorities put tags on 24 giraffes and release them. Later, they corral 1,000 giraffes; among these giraffes, 15 are tagged. To the nearest whole number, what is the best estimate for the giraffe population?


To estimate the giraffe population, we can apply the **capture-recapture** method, which is often used in ecology for estimating population sizes. The idea is that the proportion of tagged giraffes in the sample should be approximately equal to the proportion of tagged giraffes in the entire population.

We are given the following:
- \( 24 \) giraffes were initially tagged and released.
- A sample of \( 1,000 \) giraffes was later taken, and \( 15 \) of them were found to be tagged.

Let \( N \) represent the total giraffe population. According to the capture-recapture method:

\[
\frac{24}{N} = \frac{15}{1000}
\]

This equation states that the proportion of tagged giraffes in the whole population (\(\frac{24}{N}\)) is equal to the proportion of tagged giraffes in the sample (\(\frac{15}{1000}\)).

Now, solve for \( N \):

\[
\frac{24}{N} = \frac{15}{1000}
\]

Cross-multiply:

\[
24 \times 1000 = 15 \times N
\]

\[
24000 = 15N
\]

Divide both sides by \( 15 \):

\[
N = \frac{24000}{15} = 1600
\]

Thus, the best estimate for the giraffe population is \( \boxed{1600} \).

Would you like further details on this? Here are five related questions you might find useful:

1. How can we improve the accuracy of the capture-recapture method?
2. What are some limitations of the capture-recapture technique?
3. How does population growth affect capture-recapture estimates over time?
4. What other methods are used to estimate wildlife populations?
5. How do we account for migration when estimating population sizes?

**Tip**: In population studies, taking multiple samples at different times can increase the accuracy of your estimates.

A country in Africa is trying to restore its giraffe population and is carefully keeping track of how many giraffes are in the area. To do so, local wildlife authorities put tags on 24 giraffes and release them. Later, they corral 1,000 giraffes; among these giraffes, 15 are tagged. To the nearest whole number, what is the best estimate for the giraffe population?

Estimate the giraffe population in an African country using the capture-recapture method. Local wildlife authorities tagged 24 giraffes and later found 15 tagged out of 1,000 giraffes sampled. Learn how to solve this using proportions and algebra, suitable for Grades 9-12.

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