Question
Brayden was given a box of assorted chocolates for his birthday. Each night, Brayden treats himself to some chocolates. The number of chocolates remaining in the box tt days after Brayden's birthday can be modeled by the equation C, equals, minus, 3, t, plus, 12, .C=−3t+12. What is the slope of the equation and what is its interpretation in the context of the problem?
Answer
Attempt 1 out of 2
The slope of the function is
which reveals
Answer
Attempt 1 out of 2
The slope of the function is
which reveals
Answers
GPT-4o mini
To analyze the equation \( C = -3t + 12 \), let's identify the components.
In this linear equation:
- \( C \) represents the number of chocolates remaining in the box.
- \( t \) represents the number of days after Brayden's birthday.
The equation is in the slope-intercept form, \( y = mx + b \), where:
- \( m \) is the slope (which tells us the rate of change)
- \( b \) is the y-intercept (which tells us the initial value when \( t = 0 \))
From the equation \( C = -3t + 12 \):
1. The **slope** \( m \) is \(-3\).
2. The **y-intercept** \( b \) is \(12\), which means that when \( t = 0 \) (the day of Brayden's birthday), there were 12 chocolates in the box.
### Interpretation of the Slope
The slope of \(-3\) indicates that for each day \( t \) that passes, the number of chocolates \( C \) decreases by 3.
### Conclusion
The answer can be summarized as follows:
The slope of the function is \(-3\), which reveals that Brayden consumes 3 chocolates each night. Thus, every day, the number of chocolates remaining decreases by 3.
In this linear equation:
- \( C \) represents the number of chocolates remaining in the box.
- \( t \) represents the number of days after Brayden's birthday.
The equation is in the slope-intercept form, \( y = mx + b \), where:
- \( m \) is the slope (which tells us the rate of change)
- \( b \) is the y-intercept (which tells us the initial value when \( t = 0 \))
From the equation \( C = -3t + 12 \):
1. The **slope** \( m \) is \(-3\).
2. The **y-intercept** \( b \) is \(12\), which means that when \( t = 0 \) (the day of Brayden's birthday), there were 12 chocolates in the box.
### Interpretation of the Slope
The slope of \(-3\) indicates that for each day \( t \) that passes, the number of chocolates \( C \) decreases by 3.
### Conclusion
The answer can be summarized as follows:
The slope of the function is \(-3\), which reveals that Brayden consumes 3 chocolates each night. Thus, every day, the number of chocolates remaining decreases by 3.