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)

Number of mice

1

2

exponential decay function; the number of mice decreases by 75% per week, which is a constant percent rate of change

Inear 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 25 per week, which is a constant percent 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 need to look at the pattern of the decrease in numbers.

From the table:

• 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)

The number of mice decreases by a consistent amount of 25 mice each week. This indicates a constant rate of change, which is characteristic of a linear decay function.

An exponential decay function would show a percentage decrease each week, meaning the amount subtracted would progressively decrease (e.g., a percentage of the remaining mice, resulting in a rapidly decreasing number).

Therefore, the correct answer is:

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