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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. Calculate the percent decrease in the native species population between years 1 and 2, and years 2 and 3.

\begin{tabular}{|l|l|}
\hline & \multicolumn{1}{|c|}{ Population of Native Species } \\
\hline Year 1 & 7,950 \\
\hline Year 2 & 3,460 \\
\hline Year 3 & 1,380 \\
\hline
\end{tabular}

A. [tex]$49.6 \%$[/tex] and [tex]$55.3 \%$[/tex]
B. [tex]$56.5 \%$[/tex] and [tex]$60.1 \%$[/tex]
C. [tex]$52.5 \%$[/tex] and [tex]$63.3 \%$[/tex]
D. [tex]$50.4 \%$[/tex] and [tex]$68.9 \%$[/tex]
E. [tex]$54.3 \%$[/tex] and [tex]$67.6 \%$[/tex]



Answer :

GinnyAnswer
Let's carefully analyze the problem and determine the correct answer.

We have the population of a native species over three years:
- Year 1: 7,950
- Year 2: 3,460
- Year 3: 1,380

To find the percent decrease in population between two consecutive years, we use the formula for percent decrease:
[tex]\[ \text{Percent Decrease} = \left( \frac{\text{Initial Population} - \text{Final Population}}{\text{Initial Population}} \right) \times 100 \][/tex]

### Step-by-Step Solution:

1. Calculating the percent decrease from Year 1 to Year 2:
- Initial Population (Year 1): 7,950
- Final Population (Year 2): 3,460
[tex]\[ \text{Percent Decrease}_{1 \to 2} = \left( \frac{7950 - 3460}{7950} \right) \times 100 \][/tex]
- This results in approximately 56.5%.

2. Calculating the percent decrease from Year 2 to Year 3:
- Initial Population (Year 2): 3,460
- Final Population (Year 3): 1,380
[tex]\[ \text{Percent Decrease}_{2 \to 3} = \left( \frac{3460 - 1380}{3460} \right) \times 100 \][/tex]
- This results in approximately 60.1%.

### Conclusion:
By performing these calculations, we verified that the percent decrease in the native species population are:
- From Year 1 to Year 2: 56.5%
- From Year 2 to Year 3: 60.1%

Therefore, the correct answer is:

B. [tex]$56.5 \%$[/tex] and [tex]$60.1 \%$[/tex]

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