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The graph titled Height of ice sculpture shows height in inches from 0 to 30 in increments of 5 on the vertical axis and time in hours on the horizontal axis from 0 to 14 in increments of 2. The function passes through the points (0, 24) and (12, 0).

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
, as shown on the graph.

Which of the following statements is a correct interpretation of the function representing the height of the sculpture? Select all that apply.
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.
The initial height of the sculpture is 24 inches.

E.
The sculpture melts 24 inches each hour.

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

1 answer

To analyze the function representing the height of the ice sculpture, we can use the information given:

  1. The initial height of the sculpture at time 0 is given as (0, 24), which means the height starts at 24 inches.
  2. The sculpture melts to a height of 0 inches at time 12 hours (12, 0).
  3. The height decreases from 24 inches to 0 inches over 12 hours, indicating a constant rate of melting.

Let’s evaluate each statement:

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

  • Incorrect: The initial height is 24 inches.

B. The sculpture melts 2 inches each hour.

  • Incorrect: The sculpture melts from 24 inches to 0 inches over 12 hours, which means it melts 2 inches each hour, but this requires further calculation.

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

  • Incorrect: It takes 12 hours to melt completely.

D. The initial height of the sculpture is 24 inches.

  • Correct: This is true as the function starts at (0, 24).

E. The sculpture melts 24 inches each hour.

  • Incorrect: The sculpture melts a total of 24 inches over 12 hours, not 24 inches each hour.

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

  • Incorrect: The sculpture completely melts in 12 hours, not 24.

Based on the evaluations, the correct answer is:

D. The initial height of the sculpture is 24 inches.