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Use the table to answer the question. A research assistant observes that something is causing mice to die in the lab. The following table lists the number of mice at the end of each week. Week 1 2 3 4 5 Number of mice 380 355 330 305 280 Determine whether the decreasing number of mice can be modeled by a linear decay function or an exponential decay function, and why.(1 point) Responses exponential decay function; the number of mice decreases by 75% per week, which is a constant percent rate of change exponential decay function; the number of mice decreases by 75% per week, which is a constant percent rate of change exponential decay function; the number of mice decreases by 25 per week, which is a constant percent rate of change exponential decay function; the number of mice decreases by 25 per week, which is a constant percent rate of change linear decay function; the number of mice decreases by 25 per week, which is a constant rate of change linear decay function; the number of mice decreases by 25 per week, which is a constant rate of change linear decay function; the number of mice decreases by 25% per week, which is a constant rate of change linear decay function; the number of mice decreases by 25% per week, which is a constant rate of change

1 answer

To determine whether the decay of the number of mice can be modeled by a linear or exponential decay function, we need to analyze the changes in the number of mice over the weeks.

From the table:

  • Week 1: 380 mice
  • Week 2: 355 mice
  • Week 3: 330 mice
  • Week 4: 305 mice
  • Week 5: 280 mice

Now, we can calculate the change in the number of mice from one week to the next:

  • Week 1 to Week 2: 380 - 355 = 25
  • Week 2 to Week 3: 355 - 330 = 25
  • Week 3 to Week 4: 330 - 305 = 25
  • Week 4 to Week 5: 305 - 280 = 25

We see that the number of mice decreases by a constant amount of 25 each week. This indicates that the decay is linear instead of exponential since exponential decay would involve a percentage decrease, which would not yield constant absolute decreases over equal intervals.

Based on this analysis, the correct response is:

linear decay function; the number of mice decreases by 25 per week, which is a constant rate of change.