Question

the table shows the height of a candle as it is continuously burned.

candle height
\

$$\begin{array}{|c|c|} \\hline \\text{time (hours)} & \\text{height (cm)} \\\\ \\hline 0 & 25 \\\\ \\hline 0.25 & 24.375 \\\\ \\hline 0.5 & 23.75 \\\\ \\hline 0.75 & 23.125 \\\\ \\hline 1 & 22.5 \\\\ \\hline \\end{array}$$

which statement describes the candle?

• the candle starts at a height of 25 centimeters and burns at a rate of 0.625 centimeters per hour.
• the candle starts at a height of 25 centimeters and burns at a rate of 2.5 centimeters per hour.
• the candle starts at a height of 22.5 centimeters and burns at a rate of 0.625 centimeters per hour.
• the candle starts at a height of 22.5 centimeters and burns at a rate of 2.5 centimeters per hour.

Explanation:

Identify the initial height

Using the Linear Modeling knowledge point

$$ \text{At } t = 0 \text{ hours, } h = 25 \text{ cm} $$

Calculate the rate of change

Using the Slope Formula knowledge point

$$ m = \frac{22.5 - 25}{1 - 0} = -2.5 \text{ cm/hour} $$

Interpret the rate of change

Using the Rate of Change Interpretation knowledge point

$$ \text{The candle burns at a rate of } 2.5 \text{ cm/hour.} $$

Answer:

• The candle starts at a height of 25 centimeters and burns at a rate of 0.625 centimeters per hour.
• The candle starts at a height of 25 centimeters and burns at a rate of 2.5 centimeters per hour. (Correct answer)
• The candle starts at a height of 22.5 centimeters and burns at a rate of 0.625 centimeters per hour.
• The candle starts at a height of 22.5 centimeters and burns at a rate of 2.5 centimeters per hour.