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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. 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]


Sagot :

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]
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