Question
A group of Grade 11 learners were asked to investigate the number of butterflies
in a field nearby. They carried out the following steps:
● They caught and marked 18 butterflies.
● They then released them back into the field.
● Three days later, they caught 33 butterflies of which 11
were marked.
Question 3.2.1 [2 marks]
Calculate the number of butterflies that were present in the field. Show all
calculations.
Question 3.2.2 [2 marks]
List TWO precautions that the learners must consider when marking the
butterflies.
Question 3.2.3 [1 mark]
Name the method used to estimate the butterfly population.
in a field nearby. They carried out the following steps:
● They caught and marked 18 butterflies.
● They then released them back into the field.
● Three days later, they caught 33 butterflies of which 11
were marked.
Question 3.2.1 [2 marks]
Calculate the number of butterflies that were present in the field. Show all
calculations.
Question 3.2.2 [2 marks]
List TWO precautions that the learners must consider when marking the
butterflies.
Question 3.2.3 [1 mark]
Name the method used to estimate the butterfly population.
Answers
GPT-4o mini
### Question 3.2.1: Calculate the number of butterflies that were present in the field. Show all calculations.
To estimate the total number of butterflies in the field, we can use the mark-release-recapture method (also known as the Lincoln-Petersen index). The formula is:
\[
\text{Total Population} (N) = \frac{(M \times C)}{R}
\]
where:
- \(M\) = the number of marked butterflies released (18)
- \(C\) = the total number of butterflies captured in the second sample (33)
- \(R\) = the number of marked butterflies recaptured (11)
Substituting the values into the formula, we get:
\[
N = \frac{(18 \times 33)}{11}
\]
Calculating the numerator:
\[
18 \times 33 = 594
\]
Now, divide by the number of recaptured butterflies:
\[
N = \frac{594}{11} = 54
\]
Therefore, the estimated number of butterflies present in the field is **54**.
### Question 3.2.2: List TWO precautions that the learners must consider when marking the butterflies.
1. **Use Non-Toxic Marking Materials**: The learners should ensure that the materials used for marking the butterflies are non-toxic and do not harm the butterflies in any way. This could include using non-toxic paint or stickers that won’t impede their movement or ability to feed.
2. **Minimize Handling Time**: The learners should strive to handle the butterflies as little as possible to minimize stress and potential injury. Quick and gentle handling helps ensure that the butterflies can return to their natural behavior immediately after being marked.
### Question 3.2.3: Name the method used to estimate the butterfly population.
The method used to estimate the butterfly population is called the **Mark-Release-Recapture Method**.
To estimate the total number of butterflies in the field, we can use the mark-release-recapture method (also known as the Lincoln-Petersen index). The formula is:
\[
\text{Total Population} (N) = \frac{(M \times C)}{R}
\]
where:
- \(M\) = the number of marked butterflies released (18)
- \(C\) = the total number of butterflies captured in the second sample (33)
- \(R\) = the number of marked butterflies recaptured (11)
Substituting the values into the formula, we get:
\[
N = \frac{(18 \times 33)}{11}
\]
Calculating the numerator:
\[
18 \times 33 = 594
\]
Now, divide by the number of recaptured butterflies:
\[
N = \frac{594}{11} = 54
\]
Therefore, the estimated number of butterflies present in the field is **54**.
### Question 3.2.2: List TWO precautions that the learners must consider when marking the butterflies.
1. **Use Non-Toxic Marking Materials**: The learners should ensure that the materials used for marking the butterflies are non-toxic and do not harm the butterflies in any way. This could include using non-toxic paint or stickers that won’t impede their movement or ability to feed.
2. **Minimize Handling Time**: The learners should strive to handle the butterflies as little as possible to minimize stress and potential injury. Quick and gentle handling helps ensure that the butterflies can return to their natural behavior immediately after being marked.
### Question 3.2.3: Name the method used to estimate the butterfly population.
The method used to estimate the butterfly population is called the **Mark-Release-Recapture Method**.