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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 constant rate of change.
Yes, 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.

1 answer

To determine if the number of mice can be modeled by a linear function, we need to analyze the rate of growth over the weeks.

Let's examine the number of mice and see how it changes from week to week:

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

The differences in the number of mice are:

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

The changes are not constant, indicating that the growth rate is variable.

Thus, the correct response is:

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