To determine which candle will burn for the longest period of time, we need to analyze Function 1 and Function 2.
Function 1:
The height of the first candle as a function of time is given by \( f(x) = -2.5x + 25 \).
To find out how long this candle burns, we need to determine when the height reaches zero:
\[ 0 = -2.5x + 25 \]
Solving for \( x \):
\[ 2.5x = 25 \ x = \frac{25}{2.5} = 10 \]
So, the first candle burns for 10 hours.
Function 2:
We're given a graph representing the height of the second candle, but since the description does not provide specific details about the equation or the point where it reaches zero height, we'll need to make a reasonable assumption based on standard practices.
Typically, the height of the second candle would also be a linear function (like Function 1). If the graph shows a straight line that drops to the height of zero, we can look for the x-intercept to see when the candle burns out.
Without the specific numerical values or a clear mathematical representation from the graph mentioned, we cannot definitively calculate the time it burns. However, let's assume that the second candle's nature is similar and investigate the maximum height it reaches.
- If the graph shows that the second candle's height reaches zero at some point less than 10 hours, then the first candle lasts longer.
- If the second candle's height reaches zero at exactly 10 hours or more, then we would have to conclude based on what is observable.
Given that we don't have exact details on the graph for the second candle, we cannot definitively compare the two.
Conclusion:
Since we lack enough information about Function 2 to establish when it reaches a height of zero, the most accurate response based on the information provided is:
There is not enough information given to determine which candle will burn for the longest period of time.
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