Question
An ice sculpture is used as a centerpiece at a banquet. Once the sculpture is removed from the freezer it begins to melt. The height of the sculpture can be represented by the function h(t)=−2t+24
, as shown on the graph.
Which of the following statements is a correct interpretation of the function representing the height of the sculpture? Select all that apply.
(1 point)
Responses
The initial height of the sculpture is 24 inches.
The initial height of the sculpture is 24 inches.
The initial height of the sculpture is 2 inches.
The initial height of the sculpture is 2 inches.
The sculpture melts 2 inches each hour.
The sculpture melts 2 inches each hour.
It takes the sculpture 24 hours to melt completely.
It takes the sculpture 24 hours to melt completely.
The sculpture melts 24 inches each hour.
The sculpture melts 24 inches each hour.
It takes 2 hours for the sculpture to melt completely.
, as shown on the graph.
Which of the following statements is a correct interpretation of the function representing the height of the sculpture? Select all that apply.
(1 point)
Responses
The initial height of the sculpture is 24 inches.
The initial height of the sculpture is 24 inches.
The initial height of the sculpture is 2 inches.
The initial height of the sculpture is 2 inches.
The sculpture melts 2 inches each hour.
The sculpture melts 2 inches each hour.
It takes the sculpture 24 hours to melt completely.
It takes the sculpture 24 hours to melt completely.
The sculpture melts 24 inches each hour.
The sculpture melts 24 inches each hour.
It takes 2 hours for the sculpture to melt completely.
Answers
GPT-4o mini
To analyze the function \( h(t) = -2t + 24 \):
1. **The initial height of the sculpture is 24 inches.**
- **True**: When \( t = 0 \), \( h(0) = -2(0) + 24 = 24 \).
2. **The initial height of the sculpture is 2 inches.**
- **False**: The initial height is 24 inches, not 2 inches.
3. **The sculpture melts 2 inches each hour.**
- **True**: The coefficient of \( t \) is -2, indicating that the height decreases by 2 inches for each unit of time (each hour).
4. **It takes the sculpture 24 hours to melt completely.**
- **True**: To find when the sculpture melts completely, set \( h(t) = 0 \):
\[
0 = -2t + 24 \\
2t = 24 \\
t = 12 \text{ hours.}
\]
- It takes 12 hours, *not* 24 hours to melt completely, so this statement is **False**.
5. **The sculpture melts 24 inches each hour.”**
- **False**: The sculpture melts at a rate of 2 inches per hour, not 24.
6. **It takes 2 hours for the sculpture to melt completely.**
- **False**: Based on the calculations above, it takes 12 hours, not 2.
**Summary of correct statements:**
- The initial height of the sculpture is 24 inches.
- The sculpture melts 2 inches each hour.
1. **The initial height of the sculpture is 24 inches.**
- **True**: When \( t = 0 \), \( h(0) = -2(0) + 24 = 24 \).
2. **The initial height of the sculpture is 2 inches.**
- **False**: The initial height is 24 inches, not 2 inches.
3. **The sculpture melts 2 inches each hour.**
- **True**: The coefficient of \( t \) is -2, indicating that the height decreases by 2 inches for each unit of time (each hour).
4. **It takes the sculpture 24 hours to melt completely.**
- **True**: To find when the sculpture melts completely, set \( h(t) = 0 \):
\[
0 = -2t + 24 \\
2t = 24 \\
t = 12 \text{ hours.}
\]
- It takes 12 hours, *not* 24 hours to melt completely, so this statement is **False**.
5. **The sculpture melts 24 inches each hour.”**
- **False**: The sculpture melts at a rate of 2 inches per hour, not 24.
6. **It takes 2 hours for the sculpture to melt completely.**
- **False**: Based on the calculations above, it takes 12 hours, not 2.
**Summary of correct statements:**
- The initial height of the sculpture is 24 inches.
- The sculpture melts 2 inches each hour.