Question

a store sells two candles. one is 14 cm tall and burns at a constant rate of 1 cm per hour, and the second candle burns according to the function $h(t) = -0.5t + 12$, where $t$ is how long the candle burns, in hours, and $h(t)$ is the height of the candle. determine and compare the domains of the candles.

the first candle has a domain of $0 \leq t \leq 24$, and the second candle has a domain of $0 \leq t \leq 14$ the second candle has a larger domain

the first candle has a domain of $0 \leq t \leq 24$, and the second candle has a domain of $0 \leq t \leq 14$ the first candle has a larger domain

the first candle has a domain of $0 \leq t \leq 14$ and the second candle has a domain of $0 \leq t \leq 24$ the first candle has a larger domain

the first candle has a domain of $0 \leq t \leq 14$ and the second candle has a domain of $0 \leq t \leq 24$ the second candle has a larger domain

Explanation:

Step1: Find the domain of the first candle

The first candle is 14 cm tall and burns at 1 cm per hour. When \(h = 0\) (completely burned), using the formula \(h=14 - t\) (where \(h\) is height and \(t\) is time). Set \(h = 0\), then \(0=14 - t\), so \(t = 14\). The domain is \(0\leq t\leq14\) (since \(t\geq0\) and when it burns out \(t = 14\)).

Step2: Find the domain of the second candle

For the function \(h(t)=- 0.5t + 12\), when \(h(t)=0\) (completely burned), set \(0=-0.5t + 12\). Solve for \(t\):

$$
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$$

The domain is \(0\leq t\leq24\) (since \(t\geq0\) and when it burns out \(t = 24\)).

Answer:

The first candle has a domain of \(0\leq t\leq14\) and the second candle has a domain of \(0\leq t\leq24\). The second candle has a larger domain.