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Ben is trying to decide which of two candles to purchase.

The packaging for the first candle states that the height in inches of the candle as a function of time in hours is represented by Function 1.

Function 1: f(x)=−2.5x+25


The packaging for the second candle shows the height in inches of the candle as a function of time in hours is represented by the graph shown in Function 2.

Function 2:

A line is plotted on a coordinate plane. The x-axis representing hours ranges from negative 1 to 10 in one-unit increments. The y-axis representing height in inches ranges from negative 1 to 10 in one-unit increments.

Which candle will burn for the longest period of time?

(1 point)
Responses

The candles will burn for the same length of time.
The candles will burn for the same length of time.

The second candle will burn for the longest period of time.
The second candle will burn for the longest period of time.

The first candle will burn for the longest period of time.
The first candle will burn for the longest period of time.

There is not enough information given to determine which candle will burn for the longest period of time.
There is not enough information given to determine which candle will burn for the longest period of time.
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1 answer

To determine which candle will burn for the longest period of time, we need to analyze Function 1 and the provided graph for Function 2.

Function 1: The function for the first candle is given by: \[ f(x) = -2.5x + 25 \]

We can find out how long the first candle lasts by setting \( f(x) \) (the height) to zero and solving for \( x \): \[ -2.5x + 25 = 0 \] \[ -2.5x = -25 \] \[ x = \frac{25}{2.5} = 10 \]

So, the first candle will burn for 10 hours.

Function 2: For the second candle, we need to interpret the graph. Assuming that the graph is a linear function as described, we look for the point where the height (y-value) becomes zero.

Since the specifics of the graph are not available here, let's assume the line intersects the x-axis at some point. If the graph has a height of zero at a point less than 10 hours on the x-axis, then we can conclude that the second candle burns for a shorter period.

Without the exact data from the graph (the point where the line crosses the x-axis), I can't conclude definitively.

Conclusion: If the second candle burns out at a point less than 10 hours on the graph, then the first candle will last longer. If it extends beyond the x-axis, then the second candle may last longer.

Given the options again:

  • If the second candle burns out before 10 hours, select "The first candle will burn for the longest period of time."
  • If it burns out at 10 hours, select "The candles will burn for the same length of time."
  • If it extends beyond 10 hours, select "The second candle will burn for the longest period of time."
  • If unable to determine due to ambiguity, "There is not enough information given."

Since I cannot see the graph, I am unable to provide a definitive answer without further information. Please refer to the graph to see where the second candle's height reaches zero.