Use the table to answer the 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. Responses 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. - no response given 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. - no response given 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. - no response given The bear population is proportionally related to the number of years because the ratios are equivalent.

Answer 1

To determine whether the bear population is proportionally related to the number of years, we need to look at the ratio of the bear population to the time in years. Proportionality means that these ratios should be equivalent for every pair of years in the data.

Let's calculate the ratios based on the given table:

1. Year 1: Population = 6

   • Ratio = 6/1 = 6

2. Year 2: Population = 20

   • Ratio = 20/2 = 10

3. Year 3: Population = 120

   • Ratio = 120/3 = 40

4. Year 4: Population = 60

   • Ratio = 60/4 = 15

5. Year 5: Population = 240

   • Ratio = 240/5 = 48

Now let's summarize the ratios for comparison:

• Year 1: 6
• Year 2: 10
• Year 3: 40
• Year 4: 15
• Year 5: 48

Since these ratios are not all the same, the bear population is not proportionally related to the number of years.

From the responses provided:

• The correct choice would be: 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.

This response highlights that the ratios differ, confirming that the bear population does not increase in proportion to the years.