Question

brayden
6 of 6
the equation $h=32-\frac{1}{4}m$ models the height of a candle after lighting it, where $m$ represents the time the candle burns.
indicate whether each statement is true or false.

1. the height of the candle is 25 inches exactly 28 minutes after lighting it.
2. the slope of the equation is $\frac{1}{4}$, and the candle grows 1 inch every 4 minutes.
3. the candle has an initial height of 32 inches before lighting it.
4. the candle will have a height of 0 inches 32 minutes after lighting it.

Explanation:

Step1: Define given equation

The height equation is $h = 32 - \frac{1}{4}m$, where $h$ = height (inches), $m$ = time (minutes).

Step2: Test statement 1 (28 mins, 25 in)

Substitute $m=28$:
$h = 32 - \frac{1}{4}(28) = 32 - 7 = 25$

Step3: Test statement 2 (slope interpretation)

Slope is $-\frac{1}{4}$: height decreases $\frac{1}{4}$ in per min, so it shrinks 1 in every 4 mins (not grows).

Step4: Test statement 3 (initial height, m=0)

Substitute $m=0$:
$h = 32 - \frac{1}{4}(0) = 32$

Step5: Test statement 4 (32 mins, 0 in)

Substitute $m=32$:
$h = 32 - \frac{1}{4}(32) = 32 - 8 = 24$

Answer:

1. "The height of the candle is 25 inches exactly 28 minutes after lighting it." → True
2. "The slope of the equation is $-\frac{1}{4}$, and the candle grows 1 inch every 4 minutes." → False
3. "The candle has an initial height of 32 inches before lighting it." → True
4. "The candle will have a height of 0 inches 32 minutes after lighting it." → False