To analyze the situation properly, let's look at the points mentioned in the problem. The graph indicates that the height of the sculpture starts at 24 inches when time is 0 hours and decreases to 0 inches at 12 hours.
We can analyze each statement provided:
A. The initial height of the sculpture is 2 inches.
- This is incorrect. At time 0 hours, the height is 24 inches, not 2 inches.
B. The sculpture melts 2 inches each hour.
- To determine if this is true, we can see how much the height decreases over time. The height goes from 24 inches to 0 inches in 12 hours, which indicates a decrease of 24 inches over 12 hours. This results in an average decrease of: \[ \frac{24 \text{ inches}}{12 \text{ hours}} = 2 \text{ inches per hour} \] So this statement is correct.
C. It takes 2 hours for the sculpture to melt completely.
- This is incorrect. The sculpture takes 12 hours to melt completely, as indicated by the point (12, 0).
D. It takes the sculpture 24 hours to melt completely.
- This is also incorrect. As determined in the previous statement, it takes only 12 hours for the sculpture to melt completely.
Based on the analysis, the correct interpretation of the function representing the height of the sculpture is:
B. The sculpture melts 2 inches each hour.
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