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?
A.
The initial height of the sculpture is 2 inches.

B.
The sculpture melts 2 inches each hour.

C.
It takes 2 hours for the sculpture to melt completely.

D.
It takes the sculpture 24 hours to melt completely.

Answer 1

To interpret the function \( h(t) = -2t + 24 \):

- \( t \) is the time in hours.
- \( h(t) \) is the height of the sculpture in inches.
- The function has a y-intercept of 24, which represents the initial height of the ice sculpture when \( t = 0 \).
- The slope of -2 indicates that the height decreases by 2 inches for every hour that passes.

Now let's analyze the provided options:

A. The initial height of the sculpture is 2 inches.
- This is incorrect. The initial height when \( t = 0 \) is \( h(0) = -2(0) + 24 = 24 \) inches.

B. The sculpture melts 2 inches each hour.
- This is correct. The negative slope of -2 indicates that the height decreases by 2 inches for each hour.

C. It takes 2 hours for the sculpture to melt completely.
- This is incorrect. To find when the sculpture melts completely, you would set \( h(t) = 0 \):
\[
0 = -2t + 24 \implies 2t = 24 \implies t = 12 \text{ hours}.
\]

D. It takes the sculpture 24 hours to melt completely.
- This is incorrect. It takes 12 hours as calculated above.

Therefore, the correct interpretation of the function is:

**B. The sculpture melts 2 inches each hour.**