Question

Function 1: f(x) = -2.5x + 25
Function 2: is on graph with y axis is height in inches x axis represents hours
Which candle will burn for the longest period of time?
In graph (0,10),(1,9),(2,8),(3,7) etc

Answer 1

To determine which candle will burn for the longest period of time, we need to analyze the graph of Function 2 based on the points provided: (0,10), (1,9), (2,8), (3,7), etc.

From these points, we can see the pattern:

- At **0 hours**, the height of the candle is **10 inches**.
- At **1 hour**, the height is **9 inches**.
- At **2 hours**, the height is **8 inches**.
- At **3 hours**, the height is **7 inches**.
- ...

This pattern continues, indicating that the candle loses 1 inch of height per hour consistently.

Since the starting height of the candle is 10 inches, it will burn for 10 hours before it is completely gone (0 inches height).

Thus, if we compare this with Function 1, \( f(x) = -2.5x + 25 \), we can find how long that candle will burn as well by setting \( f(x) = 0 \):

\[
-2.5x + 25 = 0
\]
\[
2.5x = 25
\]
\[
x = 10
\]

The **candle represented by Function 1** burns for **10 hours** as well.

Both candles will burn for **the same duration of 10 hours**. Therefore, neither candle burns longer than the other; they both have the same burning time of 10 hours.