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Question

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. There is a line that goes diagonally from y10 to X10.

Which candle will burn for the longest period of time?

(1 point)
Responses

The first candle will burn for the longest period of time.
The first candle will burn for the longest period 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 candles will burn for the same length of time.
The candles will burn for the same length 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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Answer 1

To determine which candle will burn for the longest period of time, we can analyze the information provided.

For the first candle, the height as a function of time is given by the equation:

\[ f(x) = -2.5x + 25 \]

To find out when the candle burns out, we need to find \( x \) when \( f(x) = 0 \):

\[ 0 = -2.5x + 25 \]

Rearranging gives:

\[ 2.5x = 25 \]

\[ x = \frac{25}{2.5} = 10 \]

So the first candle will burn for 10 hours.

For the second candle, we know that its height is represented by a line plotted on a graph, but the equation of the line is not given. However, it is indicated that the line goes from (0, 10) to (10, 0). This means that the height decreases to 0 inches at 10 hours, indicating that this candle will also last until 10 hours.

Since both candles burn out at 10 hours, we can conclude:

The candles will burn for the same length of time.