To determine the percent decrease in the native species population between the given years, we need to use the formula for percent change. The formula for percent decrease is:
[tex]\[
\text{Percent Decrease} = \left( \frac{\text{Initial Population} - \text{Final Population}}{\text{Initial Population}} \right) \times 100
\][/tex]
Following this formula, we can calculate the percent decreases for the given data between the specified years.
### Percent Decrease from Year 1 to Year 2
1. Initial Population in Year 1: 7,950
2. Final Population in Year 2: 3,460
Using the formula:
[tex]\[
\text{Percent Decrease}_1 = \left( \frac{7950 - 3460}{7950} \right) \times 100
\][/tex]
3. Calculate the difference:
[tex]\[
7950 - 3460 = 4490
\][/tex]
4. Divide by the initial population:
[tex]\[
\frac{4490}{7950} = 0.5647798742138365
\][/tex]
5. Multiply by 100 to get the percent:
[tex]\[
0.5647798742138365 \times 100 = 56.477987421383645
\][/tex]
So, the percent decrease from Year 1 to Year 2 is [tex]\(56.48\%\)[/tex].
### Percent Decrease from Year 2 to Year 3
1. Initial Population in Year 2: 3,460
2. Final Population in Year 3: 1,380
Using the formula:
[tex]\[
\text{Percent Decrease}_2 = \left( \frac{3460 - 1380}{3460} \right) \times 100
\][/tex]
3. Calculate the difference:
[tex]\[
3460 - 1380 = 2080
\][/tex]
4. Divide by the initial population:
[tex]\[
\frac{2080}{3460} = 0.6011560693641618
\][/tex]
5. Multiply by 100 to get the percent:
[tex]\[
0.6011560693641618 \times 100 = 60.115606936416185
\][/tex]
So, the percent decrease from Year 2 to Year 3 is [tex]\(60.12\%\)[/tex].
### Conclusion
Based on our calculations:
- The percent decrease from Year 1 to Year 2 is [tex]\(56.48\%\)[/tex], approximately [tex]\(56.5\%\)[/tex]
- The percent decrease from Year 2 to Year 3 is [tex]\(60.12\%\)[/tex], approximately [tex]\(60.1\%\)[/tex]
Therefore, the correct answer is:
B. [tex]\(56.5\% \)[/tex] and [tex]\(60.1\%\)[/tex]
