Question

50 POINTS
A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 8 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, 8) would represent a height of 8 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)

Answer 1

Alright, let's start by setting this up as a function.

y = -.5x + 8

the negative for this function is because we know that the candle height decreases as it burns, and the 8 is for the starting height of the candle.

A.

(0, 8)
(1, 7.5)
(2, 7)
(3, 6.5)
(4, 6)
(5, 5.5)

B.

This is a function (an inverse function, to be exact). We know this because there must be exactly one output for each unique input.

C. 

It would still be a function.

(0, 8)
(1, 7.6)
(2, 7.2)
(3, 6.8)
etc...

If you need anything else, I would be happy to help!

Answer 2

Answer:

A. (0, 8) , (1, 7.5) , (2, 7) , 3, 6.5) , (4, 6) , (5, 5.5)

B. Yes

C. No

Step-by-step explanation: