Question

an 18 - inch candle is lit and burns at a constant rate of 2.25 inches per hour. make sure you have explored the applet in the previous question before answering the following questions.

• let r represent the remaining length of the candle (in inches).
• let t represent the number of hours that have elapsed since the candle was lit.

f. how tall is the candle when it has been burning for the following numbers of hours?

• when the candle has been burning for 2 hours it is
• when the candle has been burning for 3.4 hours it is
• when the candle has been burning for 5 hours it is

inches tall preview
inches tall preview
inches tall preview
g. write a formula to express the remaining length of the candle, r, in terms of t, the number of hours since the candle was lit.

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h. determine if the following statement is true or false.
selected answer v the rate of change of - 2.25 inches per hour conveys that, for any change in the amount of time the candle has been burning, the change in the height of the candle is always - 2.25 times as large.
i. solve the equation 0=-2.25t + 18 and describe what the answer represents.
the solution is t =
preview which means

• the solution describes the height of the candle when the candle is 0 inches tall.
• the solution describes the height of the candle when the candle has been burning for 8 hours.
• the solution describes how long the candle has been burning when the candle is 0 inches tall.
• the solution describes how long the candle has been burning when the candle has been burning for 8 hours.

Explanation:

Step1: Find remaining length formula

The initial length is 18 inches and it burns at 2.25 inches per hour, so $r = 18- 2.25t$.

Step2: Calculate for $t = 2$

$r=18 - 2.25\times2=18 - 4.5 = 13.5$.

Step3: Calculate for $t = 3.4$

$r=18-2.25\times3.4=18 - 7.65 = 10.35$.

Step4: Calculate for $t = 5$

$r=18-2.25\times5=18 - 11.25 = 6.75$.

Step5: Solve $0=-2.25t + 18$

$2.25t=18$, so $t=\frac{18}{2.25}=8$. It represents how long the candle has been burning when it is 0 inches tall.

Answer:

When the candle has been burning for 2 hours it is 13.5 inches tall.
When the candle has been burning for 3.4 hours it is 10.35 inches tall.
When the candle has been burning for 5 hours it is 6.75 inches tall.
Formula: $r = 18-2.25t$
The statement is true.
The solution is $t = 8$, which means the solution describes how long the candle has been burning when the candle is 0 inches tall.