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.

Question

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 \( h(t) = -2t + 24 \) properly, let's analyze it step-by-step.

1. Initial Height: When \( t = 0 \), substituting this into the function gives: \[ h(0) = -2(0) + 24 = 24 \text{ inches.} \] Thus, the initial height of the sculpture is 24 inches, not 2 inches.

2. Melting Rate: The term \(-2t\) indicates that the height is decreasing at a rate of 2 inches per hour (since \( t \) represents time in hours).

3. Time to Melt Completely: To find when the sculpture melts completely, we set \( h(t) = 0 \): \[ 0 = -2t + 24 \] Solving for \( t \): \[ -2t = -24 \implies t = 12 \text{ hours.} \] This means it takes 12 hours for the sculpture to melt completely.

Now, let's review the answer options:

A. The initial height of the sculpture is 2 inches. (Incorrect)

B. The sculpture melts 2 inches each hour. (Correct)

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

D. It takes the sculpture 24 hours to melt completely. (Incorrect)

Thus, the correct interpretation of the function is B: The sculpture melts 2 inches each hour.