Select the correct answer.

A group of scientists studied the invasion of a species in an area and its effect on the population of a native species. Study the given data and determine 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 :

Let's analyze the given data and determine the percent decrease in the population of the native species between Year 1 and Year 2, and then between Year 2 and Year 3.

### Step-by-Step Solution

1. Initial Data:
- Population in Year 1: 7,950
- Population in Year 2: 3,460
- Population in Year 3: 1,380

2. Calculate the Percent Decrease from Year 1 to Year 2:
[tex]\[ \text{Percent Decrease from Year 1 to Year 2} = \frac{\text{Population Year 1} - \text{Population Year 2}}{\text{Population Year 1}} \times 100 \][/tex]
Substituting the numbers:
[tex]\[ \text{Percent Decrease from Year 1 to Year 2} = \frac{7950 - 3460}{7950} \times 100 \][/tex]
Simplifying:
[tex]\[ \text{Percent Decrease from Year 1 to Year 2} = \frac{4490}{7950} \times 100 \approx 56.48\% \][/tex]

3. Calculate the Percent Decrease from Year 2 to Year 3:
[tex]\[ \text{Percent Decrease from Year 2 to Year 3} = \frac{\text{Population Year 2} - \text{Population Year 3}}{\text{Population Year 2}} \times 100 \][/tex]
Substituting the numbers:
[tex]\[ \text{Percent Decrease from Year 2 to Year 3} = \frac{3460 - 1380}{3460} \times 100 \][/tex]
Simplifying:
[tex]\[ \text{Percent Decrease from Year 2 to Year 3} = \frac{2080}{3460} \times 100 \approx 60.12\% \][/tex]

4. Identify the Correct Answer Choice:
- From our calculations, the percent decrease from Year 1 to Year 2 is approximately [tex]\(56.48\%\)[/tex].
- The percent decrease from Year 2 to Year 3 is approximately [tex]\(60.12\%\)[/tex].

Given these results, the correct answer matches the values calculated:

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

So, the correct answer is:
[tex]\[ \text{B. } 56.5\% \text{ and } 60.1\% \][/tex]