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

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

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

Answer 1

To determine whether the decreasing number of mice can be modeled using a linear decay function or an exponential decay function, we should first analyze the data provided:

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

1. Linear Decay Function: This implies a constant absolute decrease in the quantity.

Let’s calculate the change in the number of mice each week:

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

The number of mice decreases consistently by 25 each week, indicating a linear relationship.

2. Exponential Decay Function: This implies a constant percentage decrease in the quantity.

To check for exponential decay, we can calculate the percentage decrease each week:

• From Week 1 to Week 2: (380 - 355) / 380 * 100 = 6.58%
• From Week 2 to Week 3: (355 - 330) / 355 * 100 = 7.04%
• From Week 3 to Week 4: (330 - 305) / 330 * 100 = 7.58%
• From Week 4 to Week 5: (305 - 280) / 305 * 100 = 8.20%

The percentage decrease is not constant, indicating that we do not have an exponential decay function.

Conclusion: Since the number of mice decreases by a constant amount (25 mice per week), the appropriate model for this situation is a linear decay function.

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