To determine which candle will burn for the longest period of time, we can analyze the information given.
For the first candle:
The function given is \( f(x) = -2.5x + 25 \). This function represents the height of the candle over time in hours. To find out when the candle burns out (when the height reaches 0), we can set the function equal to 0 and solve for \( x \):
\[ 0 = -2.5x + 25 \]
\[ 2.5x = 25 \]
\[ x = \frac{25}{2.5} = 10 \]
So, the first candle will burn for 10 hours.
For the second candle:
The height of the second candle is represented by a graph. Since there isn't a direct mathematical function provided, we would typically look at where the graph intersects the x-axis (height = 0) to determine when the candle burns out. However, you haven't provided a description of the graph's properties (like maximum height and slope).
If you could see the graph, you would look for the x-coordinate at which the height becomes 0. If the candle height graphically approaches zero before 10 hours, then the first candle will last longer. If it remains above 0 at 10 hours, then that candle would last longer.
Conclusion:
Without additional details about the graph of Function 2, we cannot definitively say which candle burns longer. Therefore, the most accurate answer based on the information given is:
There is not enough information given to determine which candle will burn for the longest period of time.