To determine which candle burns for the longest period of time, we can analyze the information given in Function 1 and the graph for Function 2.
Function 1: The height of the first candle is modeled by the equation \( f(x) = -2.5x + 25 \), where \( x \) is the time in hours.
To find out when the first candle burns out, we set the height \( f(x) \) to 0 and solve for \( x \):
\[ 0 = -2.5x + 25 \] \[ 2.5x = 25 \] \[ x = \frac{25}{2.5} = 10 \]
Thus, the first candle burns out after 10 hours.
Function 2: We don't have the exact equation for Function 2, but we can analyze the graph to determine when the candle burns out. We can check the point where the height reaches 0 on the graph. If the candle's height remains positive until a certain hour (let’s say, for instance, it lasts for 8 hours before hitting 0), we can conclude from the graph.
Assuming you see from the graph that the second candle burns out earlier than 10 hours (such as 8 hours, as an example), we can conclude:
- The first candle burns out in 10 hours.
- The second candle, if it burns out at say 8 hours, will burn for a shorter time.
Therefore, without exact values from the graph in Function 2 but presuming it burns out before 10 hours, we can conclude:
The first candle will burn for the longest period of time.
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