Question

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

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
exponential decay function; the number of mice decreases by 25 per week, which is a constant percent rate of change
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Answer 1

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

1. **Linear decay function**: This type of function would show a constant amount of change in the number of mice each week. For example, if the number of mice decreases by a fixed number each week (e.g., 25 mice), it would be linear.

2. **Exponential decay function**: This type of function indicates that the number of mice decreases by a fixed percentage each week. For example, if the number of mice decreases by 25% each week, it would follow an exponential decay.

Now, let’s look at the data provided:

- Week 1: 380 mice
- Week 2: 355 mice (decrease of 25)
- Week 3: 330 mice (decrease of 25)
- Week 4: 305 mice (decrease of 25)
- Week 5: 280 mice (decrease of 25)

From the observations:
- The number of mice decreases by **25 mice** each week. This is a constant amount.

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.**