To determine the regions with the highest and lowest population densities, we will calculate the population density for each region using the formula:
[tex]\[
\text{Population Density} = \frac{\text{Population}}{\text{Area (acres)}}
\][/tex]
Let's apply this formula to each of the preserves:
1. Bear Creek Preserve, PA:
[tex]\[
\text{Population Density} = \frac{12,624}{3,412} \approx 3.6998827667057443 \text{ red foxes per acre}
\][/tex]
2. Binky Lee Preserve, PA:
[tex]\[
\text{Population Density} = \frac{462}{112} \approx 4.125 \text{ red foxes per acre}
\][/tex]
3. ChesLen Preserve, PA:
[tex]\[
\text{Population Density} = \frac{3,537}{1,263} \approx 2.8004750593824226 \text{ red foxes per acre}
\][/tex]
4. Crow's Nest Preserve, PA:
[tex]\[
\text{Population Density} = \frac{2,142}{612} \approx 3.5 \text{ red foxes per acre}
\][/tex]
Now, we can compare these densities:
- Bear Creek Preserve: [tex]\(3.6998827667057443\)[/tex]
- Binky Lee Preserve: [tex]\(4.125\)[/tex]
- ChesLen Preserve: [tex]\(2.8004750593824226\)[/tex]
- Crow's Nest Preserve: [tex]\(3.5\)[/tex]
From these calculations, we see that the region with the highest population density is Binky Lee Preserve, PA with a density of [tex]\(4.125\)[/tex] red foxes per acre. The region with the lowest population density is ChesLen Preserve, PA with a density of [tex]\(2.8004750593824226\)[/tex] red foxes per acre.
Therefore:
- The region with the highest population density is [tex]\( \boxed{\text{Binky Lee Preserve, PA}} \)[/tex].
- The region with the lowest population density is [tex]\( \boxed{\text{ChesLen Preserve, PA}} \)[/tex].
