Question
Which situation below would describe a negative Rate of Change over time.
For every text message you send, your bill goes up by $.08. You keep track of your texts in a table to find the total amount of your monthly bill.
Your speed of walking to school is 12 minutes per mile. You walk 2 miles. You graph your distance walked.
You owe your sister $40 and each week you pay her $5. You track your total amount owed in a table.
For every text message you send, your bill goes up by $.08. You keep track of your texts in a table to find the total amount of your monthly bill.
Your speed of walking to school is 12 minutes per mile. You walk 2 miles. You graph your distance walked.
You owe your sister $40 and each week you pay her $5. You track your total amount owed in a table.
Answers
GPT-4o mini
A negative rate of change indicates that a quantity is decreasing over time.
In the situations described:
1. **Text Message Bill**: For every text message sent, the bill increases by $0.08. This represents a positive rate of change since the total bill is increasing with more text messages.
2. **Walking to School**: The speed of walking is given as 12 minutes per mile. This indicates a positive rate of distance covered over time, as you are still walking and accumulating distance.
3. **Owing Your Sister Money**: You owe your sister $40, and for each week you pay her $5. As you pay her, the total amount you owe decreases. This represents a negative rate of change because the amount owed is decreasing over time.
Thus, the situation that describes a **negative rate of change over time** is:
**You owe your sister $40 and each week you pay her $5. You track your total amount owed in a table.**
In the situations described:
1. **Text Message Bill**: For every text message sent, the bill increases by $0.08. This represents a positive rate of change since the total bill is increasing with more text messages.
2. **Walking to School**: The speed of walking is given as 12 minutes per mile. This indicates a positive rate of distance covered over time, as you are still walking and accumulating distance.
3. **Owing Your Sister Money**: You owe your sister $40, and for each week you pay her $5. As you pay her, the total amount you owe decreases. This represents a negative rate of change because the amount owed is decreasing over time.
Thus, the situation that describes a **negative rate of change over time** is:
**You owe your sister $40 and each week you pay her $5. You track your total amount owed in a table.**