Question

Time (years) Bear Population
1 6
20 120
60 240
One biologist claimed that the bear population was proportionally related to the number of years after they were reintroduced into the wild. Based on the information in the table, would you agree? Explain your answer.

(1 point)
Responses

The bear population is proportionally related to the number of years because the ratios are equivalent.
The bear population is proportionally related to the number of years because the ratios are equivalent.

The bear population is not proportionally related to the number of years because the ratios are equivalent.
The bear population is not proportionally related to the number of years because the ratios are equivalent.

The bear population is proportionally related to the number of years because the ratios are not equivalent.
The bear population is proportionally related to the number of years because the ratios are not equivalent.

The bear population is not proportionally related to the number of years because the ratio in the last row is not equal to the ratios in the first two rows.
The bear population is not proportionally related to the number of years because the ratio in the last row is not equal to the ratios in the first two rows.
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Answer 1

To determine whether the bear population is proportionally related to the number of years based on the information provided in the table, we can look at the ratios of the bear population to the number of years. Specifically, we can calculate the ratio \( \frac{\text{Bear Population}}{\text{Years}} \) for each set of values:

1. For years = 1, bear population = 6:
\[
\frac{6}{1} = 6
\]

2. For years = 20, bear population = 120:
\[
\frac{120}{20} = 6
\]

3. For years = 60, bear population = 240:
\[
\frac{240}{60} = 4
\]

Now examining the calculated ratios:
- The ratio for the first row is 6.
- The ratio for the second row is also 6.
- The ratio for the third row is 4.

Since the ratios are not all equivalent, this means that the bear population is not proportionally related to the years because the relationship does not maintain a consistent ratio across all data points.

Thus, the correct response is:

**The bear population is not proportionally related to the number of years because the ratio in the last row is not equal to the ratios in the first two rows.**