Tariq just lit a new candle and then let it burn all the way down to nothing. The initial length of the candle was 10 inches and after burning for 4 hours, the candle's height was down to 5 inches. Write an equation for L, commaL, in terms of t, commat, representing the length of the candle remaining unburned, in inches, tt hours after the candle was lit.


To model the length of the candle remaining unburned over time, we can first determine the rate at which the candle burns.

1. **Initial length of the candle**: \( L_0 = 10 \) inches
2. **Length after 4 hours**: \( L(4) = 5 \) inches

The candle burned 5 inches in 4 hours, so the rate of burning can be calculated as follows:

\[
\text{Rate of burn} = \frac{L_0 - L(4)}{4 \text{ hours}} = \frac{10 - 5}{4} = \frac{5}{4} \text{ inches per hour}
\]

The equation for the length \( L(t) \) of the candle remaining after \( t \) hours can be expressed as:

\[
L(t) = L_0 - \text{(Rate of burn)} \times t
\]

Substituting in the values:

\[
L(t) = 10 - \frac{5}{4}t
\]

Thus, the equation for the length of the candle remaining unburned, in inches, \( L(t) \) after \( t \) hours is:

\[
L(t) = 10 - \frac{5}{4}t
\]

### Questions:
1. How long will it take for the candle to completely burn down?
2. What will be the height of the candle after 6 hours?
3. If the candle burns for 10 hours, how much will be left?
4. Can you describe how the rate of burn affects the candle's total burn time?
5. What happens to the equation if the candle burns at a different rate?

### Tip:
When creating linear equations based on real-world scenarios, always ensure to identify key points and rates of change for accurate modeling.

Tariq just lit a new candle and then let it burn all the way down to nothing. The initial length of the candle was 10 inches and after burning for 4 hours, the candle's height was down to 5 inches. Write an equation for L, in terms of t, representing the length of the candle remaining unburned, in inches, t hours after the candle was lit.

Discover how to model the burn rate of a candle using the equation L(t) = 10 - (5/4)t. This problem illustrates key concepts in linear functions and rate of change, suitable for Grades 6-8.

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