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 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.

The candles will burn for the same length of time.

1 answer

To determine which candle burns for the longest period of time, we need to analyze the functions provided.

For the first candle (Function 1): The function is given as \( f(x) = -2.5x + 25 \). This function describes the height of the candle over time.

  1. To find when the candle is completely burned out, we set the height \( f(x) = 0 \): \[ -2.5x + 25 = 0 \] \[ 2.5x = 25 \] \[ x = \frac{25}{2.5} = 10 \]

So the first candle will burn for 10 hours.

For the second candle (Function 2): Since the details of the graph for Function 2 are not provided in a numerical format, we assume it has a linear relationship similar to Function 1. If the height reaches 0 at a point on the x-axis (time), that point indicates how long the candle burns.

Assuming you can visually see where the line intersects the x-axis, if the intersection occurs before 10 hours, the first candle lasts longer; if it intersects after 10 hours, the second candle lasts longer; and if it intersects at 10 hours, they last the same time.

Given the information available to us, if the graph of Function 2 shows that the candle height reaches 0 before 10 hours (which is likely if the maximum height is lower than that of Function 1), we can conclude accordingly.

Conclusion: Without seeing the graph of Function 2, we cannot definitively state which candle burns longer.

If you can state that the graph intersects at a time greater than 10 hours, then the second candle burns the longest. If it intersects at less than 10 hours, then the first candle burns the longest.

It appears that the best answer based on the context given would be either:

  • There is not enough information given to determine which candle will burn for the longest period of time. (If you lack specific data about Function 2)

or

  • The first candle will burn for the longest period of time. (if the second candle's graph indicates it burns out before 10 hours)

You need to check where Function 2 intersects the x-axis to provide a clear answer.