Question
Multiple.
Choice question the graph titled. Hide a vice sculpture shows height and inches from 0 to 30 and increments of 5 on the vertical Axis and time and hours on the horizontal Axis and time and hours on the horizontal Axis from 0 to 14 and increments of 2. The function passes through the points 024 and 120 and ice sculpture is used as a Central piece 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 age (T) equals −2T plus 24, as shown on the graph, which of the following statements is a correct interpretation of the function representing the height of the sculpture is 2 inches B. The sculpture melts 2 inches each hour. It takes 2 hours for the sculpture to melt completely.D it takes the sculpture twenty four hours to melt completely
Choice question the graph titled. Hide a vice sculpture shows height and inches from 0 to 30 and increments of 5 on the vertical Axis and time and hours on the horizontal Axis and time and hours on the horizontal Axis from 0 to 14 and increments of 2. The function passes through the points 024 and 120 and ice sculpture is used as a Central piece 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 age (T) equals −2T plus 24, as shown on the graph, which of the following statements is a correct interpretation of the function representing the height of the sculpture is 2 inches B. The sculpture melts 2 inches each hour. It takes 2 hours for the sculpture to melt completely.D it takes the sculpture twenty four hours to melt completely
Answers
GPT-4o mini
To interpret the function \( h(t) = -2t + 24 \) correctly based on the information provided about the ice sculpture melting:
1. **Understanding the function**:
- The function describes the height of the sculpture (in inches) as a function of time (in hours).
- The coefficient of \( t \) is -2, indicating that for each hour (as time increases), the height of the sculpture decreases by 2 inches.
- The initial height of the sculpture, when \( t = 0 \), is 24 inches.
2. **Analyzing the options**:
- **A. The height of the sculpture is 2 inches.**: This is incorrect as the height decreases over time.
- **B. The sculpture melts 2 inches each hour.**: This is correct since the coefficient \(-2\) indicates a decrease of 2 inches for each hour.
- **C. It takes 2 hours for the sculpture to melt completely.**: This is incorrect as the initial height is 24 inches, and it would take 12 hours (24 inches / 2 inches per hour) to melt completely.
- **D. It takes the sculpture twenty-four hours to melt completely.**: This is also incorrect. Again, it takes 12 hours, not 24.
Given this analysis, the correct interpretation based on the height function is:
**B. The sculpture melts 2 inches each hour.**
1. **Understanding the function**:
- The function describes the height of the sculpture (in inches) as a function of time (in hours).
- The coefficient of \( t \) is -2, indicating that for each hour (as time increases), the height of the sculpture decreases by 2 inches.
- The initial height of the sculpture, when \( t = 0 \), is 24 inches.
2. **Analyzing the options**:
- **A. The height of the sculpture is 2 inches.**: This is incorrect as the height decreases over time.
- **B. The sculpture melts 2 inches each hour.**: This is correct since the coefficient \(-2\) indicates a decrease of 2 inches for each hour.
- **C. It takes 2 hours for the sculpture to melt completely.**: This is incorrect as the initial height is 24 inches, and it would take 12 hours (24 inches / 2 inches per hour) to melt completely.
- **D. It takes the sculpture twenty-four hours to melt completely.**: This is also incorrect. Again, it takes 12 hours, not 24.
Given this analysis, the correct interpretation based on the height function is:
**B. The sculpture melts 2 inches each hour.**