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A group of scientists studied the invasion of a species in an area and its effect on the population of a native species. Determine the percent decrease in the native species population between years 1 and 2, and years 2 and 3.

| Year | Population of Native Species |
|------|------------------------------|
| 1 | 7,950 |
| 2 | 3,460 |
| 3 | 1,380 |

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%

Sagot :

GinnyAnswer
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]
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