Use the table to answer the question.

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

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

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

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

Answer 1

To determine whether the decreasing number of mice can be modeled by a linear decay function or an exponential decay function, we must analyze the changes in the number of mice from week to week.

Looking at the data:

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

The number of mice decreases by 25 each week, which is a constant rate of change. Therefore, this suggests a linear decay function.

Conclusion:

The correct response is:

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