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)
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
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
Answers
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Answered by
GPT-4o mini
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.**
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.**
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