Alright, let's determine the percent decrease in the native species population between years 1 and 2, and between years 2 and 3.
1. Population Values:
- Year 1: 7,950
- Year 2: 3,460
- Year 3: 1,380
2. Percent Decrease Calculation:
a. Percent Decrease between Year 1 and Year 2:
- Initial population (Year 1): [tex]\( 7,950 \)[/tex]
- New population (Year 2): [tex]\( 3,460 \)[/tex]
The formula for percent decrease is:
[tex]\[
\text{Percent Decrease} = \left( \frac{\text{Initial Population} - \text{New Population}}{\text{Initial Population}} \right) \times 100
\][/tex]
Applying the values:
[tex]\[
\text{Percent Decrease} = \left( \frac{7,950 - 3,460}{7,950} \right) \times 100 \approx 56.48\%
\][/tex]
b. Percent Decrease between Year 2 and Year 3:
- Initial population (Year 2): [tex]\( 3,460 \)[/tex]
- New population (Year 3): [tex]\( 1,380 \)[/tex]
Applying the values similarly:
[tex]\[
\text{Percent Decrease} = \left( \frac{3,460 - 1,380}{3,460} \right) \times 100 \approx 60.12\%
\][/tex]
3. Matching the Percent Decrease with Options:
- Given the calculated percent decreases are approximately 56.48% for the period between Year 1 and Year 2, and 60.12% for the period between Year 2 and Year 3.
Comparing these with the provided options:
A. 49.6% and 55.3%
B. 56.5% and 60.1%
C. 52.5% and 63.3%
D. 50.4% and 68.9%
E. 54.3% and 67.6%
The closest match is:
B. 56.5% and 60.1%
Therefore, the percent decrease in the native species population is approximately 56.5% between years 1 and 2, and 60.1% between years 2 and 3, making option B the correct answer.
