Let's work through the problem step by step, starting with the population of wolves.
For the wolves:
- Birth rate: 4
- Death rate: 3
- Immigration: 2
- Emigration: 3
The formula to calculate the population growth is:
[tex]\[ \text{Population Growth} = (\text{Birth Rate} - \text{Death Rate}) + (\text{Immigration} - \text{Emigration}) \][/tex]
Filling in the values:
[tex]\[ \text{Population Growth} = (4 - 3) + (2 - 3) \][/tex]
Now, calculate each part:
[tex]\[ 4 - 3 = 1 \][/tex]
[tex]\[ 2 - 3 = -1 \][/tex]
Adding these parts together:
[tex]\[ 1 + (-1) = 0 \][/tex]
So, the population growth for wolves is [tex]\(0\)[/tex].
Since the population growth is [tex]\(0\)[/tex], the population is stable.
Now, let's move on to the population of deer.
For the deer:
- Birth rate: 5
- Death rate: 4
- Immigration: 8
- Emigration: 6
Using the same formula:
[tex]\[ \text{Population Growth} = (\text{Birth Rate} - \text{Death Rate}) + (\text{Immigration} - \text{Emigration}) \][/tex]
Filling in the values:
[tex]\[ \text{Population Growth} = (5 - 4) + (8 - 6) \][/tex]
Now, calculate each part:
[tex]\[ 5 - 4 = 1 \][/tex]
[tex]\[ 8 - 6 = 2 \][/tex]
Adding these parts together:
[tex]\[ 1 + 2 = 3 \][/tex]
So, the population growth for deer is [tex]\(3\)[/tex].
Since the population growth is [tex]\(3\)[/tex], the population is growing.
Summarizing all:
- For wolves:
[tex]\[
4 - 3 + 2 - 3 = 0 \\
\text{Since the population growth is } 0 \text{, the population is stable.}
\][/tex]
- For deer:
[tex]\[
5 - 4 + 8 - 6 = 3 \\
\text{Since the population growth is } 3 \text{, the population is growing.}
\][/tex]
