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.
(what i wrote for part A:A. 1. (1, 9.5): After one hour, the candle burns down by 0.5 inches, so the height becomes 10 - 0.5 = 9.5 inches.
2. (2, 9): After two hours, the candle burns down by another 0.5 inches, so the height becomes 9.5 - 0.5 = 9 inches.
3. (3, 8.5): After three hours, the candle burns down by another 0.5 inches, so the height becomes 9 - 0.5 = 8.5 inches.
4. (4, 8): After four hours, the candle burns down by another 0.5 inches, so the height becomes 8.5 - 0.5 = 8 inches.
5. (5, 7.5): After five hours, the candle burns down by another 0.5 inches, so the height becomes 8 - 0.5 = 7.5 inches.
6. (6, 7): After six hours, the candle burns down by the final 0.5 inches, so the height becomes 7.5 - 0.5 = 7 inches.
I obtained these ordered pairs by subtracting 0.5 inches from the previous height of the candle after each hour.)
Your explanation for obtaining the ordered pairs is correct. Each ordered pair represents the height of the candle after a specific number of hours, with the height decreasing by 0.5 inches each hour.
For part B:
Yes, this relation is a function. Each input value (x) corresponds to a unique output value (y). There is only one height for each specific time.
For part C:
Yes, the relation would still be a function if the rate at which the candle burned was 0.4 inches per hour instead of 0.5 inches per hour. The input and output values would remain the same, with the height decreasing by 0.4 inches each hour instead of 0.5 inches. Each input value would still correspond to a unique output value, so the relation would still be a function.