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.
Question 3.3
The graph below shows the population growth of a colony of ants.
Question 3.3.1 [1 mark]
What type of growth curve is shown in the graph?
Question 3.3.2 [3 marks]
Which phase (A, B, C or D) has the following characteristics?
a. The population grows slowly because of the new environment
b. The phase where growth takes place rapidly because there are no limiting
factors
c. Population growth slows down
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.
Question 3.3
The graph below shows the population growth of a colony of ants.
Question 3.3.1 [1 mark]
What type of growth curve is shown in the graph?
Question 3.3.2 [3 marks]
Which phase (A, B, C or D) has the following characteristics?
a. The population grows slowly because of the new environment
b. The phase where growth takes place rapidly because there are no limiting
factors
c. Population growth slows down
Answers
GPT-4o mini
### Question 3.2.1
To estimate the number of butterflies present in the field, we can use the capture-recapture method. The formula for estimating the population size (N) is:
\[
N = \frac{(M \times C)}{R}
\]
Where:
- \(M\) = number of marked individuals (18 butterflies)
- \(C\) = total number of individuals captured in the second sample (33 butterflies)
- \(R\) = number of marked individuals recaptured (11 butterflies)
Substituting the values into the formula:
\[
N = \frac{(18 \times 33)}{11}
\]
Calculating:
\[
N = \frac{594}{11}
\]
\[
N = 54
\]
Thus, **the estimated number of butterflies present in the field is 54.**
### Question 3.2.2
Two precautions that the learners must consider when marking the butterflies are:
1. Use a non-toxic and safe method for marking that does not harm the butterflies or affect their behavior.
2. Ensure that the marking does not impede the butterflies' ability to fly, forage, or escape from predators.
### Question 3.2.3
The method used to estimate the butterfly population is called the **mark-recapture method**.
---
### Question 3.3.1
The type of growth curve shown in the graph is typically known as **logistic growth**, which exhibits an S-shaped curve.
### Question 3.3.2
The phases correspond to the following characteristics:
a. **The population grows slowly because of the new environment**: This is characteristic of **Phase A** (Lag phase).
b. **The phase where growth takes place rapidly because there are no limiting factors**: This is characteristic of **Phase B** (Exponential phase).
c. **Population growth slows down**: This is characteristic of **Phase C** (Deceleration phase).
To estimate the number of butterflies present in the field, we can use the capture-recapture method. The formula for estimating the population size (N) is:
\[
N = \frac{(M \times C)}{R}
\]
Where:
- \(M\) = number of marked individuals (18 butterflies)
- \(C\) = total number of individuals captured in the second sample (33 butterflies)
- \(R\) = number of marked individuals recaptured (11 butterflies)
Substituting the values into the formula:
\[
N = \frac{(18 \times 33)}{11}
\]
Calculating:
\[
N = \frac{594}{11}
\]
\[
N = 54
\]
Thus, **the estimated number of butterflies present in the field is 54.**
### Question 3.2.2
Two precautions that the learners must consider when marking the butterflies are:
1. Use a non-toxic and safe method for marking that does not harm the butterflies or affect their behavior.
2. Ensure that the marking does not impede the butterflies' ability to fly, forage, or escape from predators.
### Question 3.2.3
The method used to estimate the butterfly population is called the **mark-recapture method**.
---
### Question 3.3.1
The type of growth curve shown in the graph is typically known as **logistic growth**, which exhibits an S-shaped curve.
### Question 3.3.2
The phases correspond to the following characteristics:
a. **The population grows slowly because of the new environment**: This is characteristic of **Phase A** (Lag phase).
b. **The phase where growth takes place rapidly because there are no limiting factors**: This is characteristic of **Phase B** (Exponential phase).
c. **Population growth slows down**: This is characteristic of **Phase C** (Deceleration phase).