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

Question

, 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 \( h(t) = -2t + 24 \), we can analyze its components:

1. The function's output, \( h(t) \), represents the height of the sculpture at time \( t \) (where \( t \) is in hours).
2. The term \( -2t \) indicates that the height decreases by 2 inches for each hour that passes.
3. The constant term \( 24 \) represents the initial height of the sculpture when \( t = 0 \).

Now, let's evaluate each option:

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

B. The sculpture melts 2 inches each hour.
This is correct. The slope of the function indicates a decrease of 2 inches per hour.

C. It takes 2 hours for the sculpture to melt completely.
This is incorrect. To find when the sculpture melts completely (when \( h(t) = 0 \)): \[ 0 = -2t + 24 \ 2t = 24 \ t = 12 \text{ hours} \] So it takes 12 hours to melt completely, not 2.

D. It takes the sculpture 24 hours to melt completely.
This is incorrect. As calculated above, it takes 12 hours to melt completely.

The correct interpretation is:
B. The sculpture melts 2 inches each hour.