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Use the table to answer the question.

A research assistant is breeding mice to use in the lab. The following table lists the number of mice at the end of each week.

Week 1 2 5 9 11
Number of mice 24 48 120 216 264
Can the number of mice be modeled by a linear function?

(1 point)
Responses

No, because the rate of growth is a constant rate of change.
No, because the rate of growth is a constant rate of change.

Yes, because the rate of growth is a variable rate of change.
Yes, because the rate of growth is a variable rate of change.

No, because the rate of growth is a variable rate of change.
No, because the rate of growth is a variable rate of change.

Yes, because the rate of growth is a constant rate of change.

1 answer

To determine if the number of mice can be modeled by a linear function, we need to check if the rate of change in the number of mice is constant over the given weeks.

Let's analyze the data from the table:

  • From Week 1 (24 mice) to Week 2 (48 mice): Change = 48 - 24 = 24
  • From Week 2 (48 mice) to Week 5 (120 mice): Change = 120 - 48 = 72
  • From Week 5 (120 mice) to Week 9 (216 mice): Change = 216 - 120 = 96
  • From Week 9 (216 mice) to Week 11 (264 mice): Change = 264 - 216 = 48

Now we can summarize the rate of change between each interval:

  • Week 1 to Week 2: 24
  • Week 2 to Week 5: 72
  • Week 5 to Week 9: 96
  • Week 9 to Week 11: 48

Since the rates of change are not constant (they vary from 24 to 72 to 96 to 48), the growth of the number of mice is not linear.

Thus, the correct response is:

No, because the rate of growth is a variable rate of change.