To determine the percent decrease in the population of a native species between years 1 and 2, and between years 2 and 3, follow these steps:
1. Calculate the percent decrease between Year 1 and Year 2:
- Initial population in Year 1: 7,950
- Population in Year 2: 3,460
The percent decrease can be found using the formula:
[tex]\[
\text{Percent Decrease} = \left( \frac{\text{Initial Population} - \text{New Population}}{\text{Initial Population}} \right) \times 100
\][/tex]
Plugging in the values:
[tex]\[
\text{Percent Decrease} = \left( \frac{7950 - 3460}{7950} \right) \times 100
\][/tex]
[tex]\[
\text{Percent Decrease} = \left( \frac{4490}{7950} \right) \times 100
\][/tex]
[tex]\[
\text{Percent Decrease} \approx 56.48\%
\][/tex]
2. Calculate the percent decrease between Year 2 and Year 3:
- Initial population in Year 2: 3,460
- Population in Year 3: 1,380
Using the same formula for percent decrease:
[tex]\[
\text{Percent Decrease} = \left( \frac{3460 - 1380}{3460} \right) \times 100
\][/tex]
[tex]\[
\text{Percent Decrease} = \left( \frac{2080}{3460} \right) \times 100
\][/tex]
[tex]\[
\text{Percent Decrease} \approx 60.12\%
\][/tex]
Therefore, the percent decrease in the population of the native species is approximately:
- 56.48% between years 1 and 2
- 60.12% between years 2 and 3
Given the possible answer choices, the correct answer is:
B. [tex]$56.5 \%$[/tex] and [tex]$60.1 \%$[/tex]
