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 \( h(t) = -2t + 24 \) 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.