A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 10 inches.
Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 10) would represent a height of 10 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points)
Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A. (2 points)
Part C: If the rate at which the candle burned was 0.4 inches per hour instead of 0.5 inches per hour, would the relation be a function? Explain your answer using input and output values. (3 points)
Part A:
To obtain the ordered pairs, we need to determine the height of the candle at different time points.
Starting from the first hour after it started burning, we can subtract 0.5 inches for each subsequent hour to find the new height.
Ordered pairs:
(1, 9.5)
(2, 9)
(3, 8.5)
(4, 8)
(5, 7.5)
(6, 7)
Part B:
Yes, the relation is a function because each input (time in hours) has a unique output (height of the candle). In other words, for every x-value in the ordered pairs, there is only one y-value.
Part C:
If the rate at which the candle burned was 0.4 inches per hour instead of 0.5 inches per hour, the relation would still be a function. The input (time in hours) would still have a unique output (height of the candle) for each x-value in the ordered pairs. The only difference would be that the rate of decrease in height would be slower, resulting in different y-values for each x-value compared to the original relation.