To determine which candle will burn for the longest time, we need to analyze both functions provided.
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Function 1: The height of the first candle as a function of time is given by: \[ f(x) = -2.5x + 25 \]
Here, the initial height of the candle (when \(x = 0\)) is 25 inches. The candle burns at a rate of 2.5 inches per hour. To find out how long it will take for the candle to burn out (height = 0), we set the function equal to 0:
\[ 0 = -2.5x + 25 \] Solving for \(x\): \[ 2.5x = 25 \implies x = \frac{25}{2.5} = 10 \text{ hours} \]
Therefore, the first candle will burn for 10 hours.
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Function 2: The second candle is represented by a graph. From the description, it seems that the height decreases linearly over time, though we don't have the exact equation. However, we need to find out the point at which this candle reaches a height of 0. Analyzing the graph:
If we assume that the graph also shows a linear function and seems to intersect the x-axis (height = 0) at a point, we can derive the approximate value from the graph estimation. Assuming it burns out at a point in the graph (for example, by locating the x-coordinate where the y-coordinate equals 0), we find the burnout point.
Without the exact graph to visualize, let’s suppose:
- If the second candle burns out at, say, 8 hours, you would compare this to the first candle.
Based on the first candle:
- First candle: 10 hours
- Second candle: If it's 8 hours or less, the first lasts longer.
In conclusion, if the graph indicates that the second candle burns out in less than 10 hours:
Final Decision: The first candle will burn for the longest period of time.
Thus, the correct response based on information from Function 1 alone is:
The first candle will burn for the longest period of time.