Question

Will fan and medal
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.

Answer 1

You could represent this using a linear function

y = m(x)+b

where the height is initially 8 inches.

if the candle is decreasing at a rate of 0.5 inches per hour. how do you think we could represent this?

Answer 2

@ladylauren

Answer 3

so you subtract 0.5 every hour

Answer 4

well look at it this way. each hour we know that the height is decreasing by 0.5 inches.

so

after x amount of hours the height decreases by 0.5(x)

follow?

Answer 5

yes

Answer 6

but we also know that the height can't keep decreasing forever. it's going to stop after a while once it reaches 8 inches. but we know that the height is initially 8 inches.

y = 8-0.5(x)

Answer 7

so we subtract 0.5 6 times?

Answer 8

On the y axis is the height of the candle, on the x axis it's the amount of hours.

Answer 9

what i'm saying here is that we can build a function that represents the candle height and time

Answer 10

ok

Answer 11

Now for your ordered pairs you can plug in any x value into this equation starting from x = 0 and then plot the points.

\[y_{1} = 8-0.5x \]

Answer 12

ok so it would be 7.5

Answer 13

after that

Answer 14

have you learned about linear equations like in the form of a line?

Answer 15

yes

Answer 16

now you have a function that represents the height of the candle as a function of time.

now let's find the height of the candle at 0 hours

so in zero hours right, we can plug in zero into our equation.

\[8-(0)*\frac{ 1 }{ 2 } = 8~inches \]

we get 8 inches. this makes sense.

now what about after an hour? we plug in 1 where we see x and get 7.5 inches.

\[8-(1)*\frac{ 1 }{ 2 } = 7.5~inches \]

Here are our points so far

(0,8)
(1,7.5)

can you see the pattern and continue from there?

Answer 17

so it is (0.8),(1,7.5),(2,7),(3,6.5),(4,6),(5,5.5)

Answer 18

Yes, and all the information about this is contained in our equation

Answer 19

ok

Answer 20

what do you notice about the height after each hour just by looking at the points.

Answer 21

can you help me with part 2

Answer 22

it decreases 0.5 every hour
and they are on a straight line so it is liner

Answer 23

yes. I'll give you a hint but not the answer

Answer 24

ok

Answer 25

Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A.

Answer 26

What do you think?

Answer 27

i think it would be a linear function

Answer 28

okay, but why?

Answer 29

because when i put it on a graph it is in a straight line

Answer 30

that's one reason

Answer 31

the other reason is that in every function three must be one only x value for every y value

Answer 32

ok like in function 1 input for each output

Answer 33

another way we can actually test this by placing a vertical line through our function like this.

can you see why one is a function and not the other?

Answer 34

cause the line on the function is straight and the other one isent

Answer 35

Well, yes kind of. if you notice that for the circle the line passes through two points. one x value has two y values It can't be a function .

Answer 36

oh i see now

Answer 37

thank you so much this was realy helpfull

Answer 38

no problem