(04.01 MC) 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 0.75 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)

Respuesta :

The ordered pairs, justification of the function with different order pairs is required.

The ordered pairs are [tex](0,10),(1,9.5),(2,9),(3,8.5),(4,8),(5,7.5)[/tex]

All values of [tex]x[/tex] has a unique value in [tex]y[/tex] so, it is a function.

y = Height of candle

x = Number of hours

m = Rate = 0.5 inches per hour

c = y intercept = Initial height = 10 inches

The required function is

[tex]y=-0.5x+10[/tex]

Six ordered pairs would be

[tex]x=0,1,2,3,4,5[/tex]

[tex]y=-0.5\times 0+10=10[/tex]

[tex]y=-0.5\times 1+10=9.5[/tex]

[tex]y=-0.5\times 2+10=9[/tex]

[tex]y=-0.5\times 3+10=8.5[/tex]

[tex]y=-0.5\times 4+10=8[/tex]

[tex]y=-0.5\times 5+10=7.5[/tex]

The ordered pairs are

[tex](0,10),(1,9.5),(2,9),(3,8.5),(4,8),(5,7.5)[/tex]

It can be seen that all values of [tex]x[/tex] has a unique value in [tex]y[/tex] so, it is a function.

If m = 0.75 inches per hour

The function would change to

[tex]y=-0.75x+10[/tex]

Some ordered pairs would be

[tex]y=-0.75\times 0+10[/tex]

[tex]y=-0.75\times 1+10[/tex]

[tex](0,10),(1,9.25)[/tex]

The same is seen in this function, all values of [tex]x[/tex] has a unique value in [tex]y[/tex] so, it is a function.

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