Question

Will Give Medal!!!!

Answer 1

4. Fiber-optic cables are used widely for Internet wiring, data transmission, and surgeries. When light passes through a fiber-optic cable, its intensity decreases with the increase in the length of the cable. If 1,500 lumens of light enter the cable, the intensity of light decreases by 3.4% per meter of cable.


Part A: Can this situation be represented by a linear function? Justify your answer. (2 points)

Part B: Write a function f(x) to represent the intensity of light, in lumens, when it has passed through x meters of the cable. (4 points)

Part C: Some scientists are trying to make a cable for which the intensity of light would decrease by 5 lumens per unit length of the cable. Can this situation be represented by a linear function? Justify your answer and write the appropriate function to represent this situation if 1500 lumens of light enter the cable. (4 points)

Part A: Can this situation be linear? Why or why not?

Part B:
Write the function: f(x) =

Part C:
Some scientists are trying to make a cable for which the intensity of light would decrease by 5 lumens per unit length of the cable. Is this a linear function?

Why or why not?

Write the function: f(x) =

Answer 2

for

Answer 3

These are the ones im supposed to do btw:
Part A: Can this situation be linear? Why or why not?

Part B:
Write the function: f(x) =

Part C:
Some scientists are trying to make a cable for which the intensity of light would decrease by 5 lumens per unit length of the cable. Is this a linear function?

Why or why not?

Write the function: f(x) =

Answer 4

@mathmath333

Answer 5

love your pic btw

Answer 6

haha I like yours too @mclover1477

Answer 7

phanks

Answer 8

and i spelt it like that on purpose

Answer 9

yeah I know!

Answer 10

@mathmate

Answer 11

It's long. Looks like it takes me days to read the question, but I'll try!

Answer 12

thank you!

Answer 13

Yes, it is very informative, so I didn't waste my investment in time.
Now your turn, let's do it one by one.
What is your proposed answer for A? (The more you explain, the more help you get!)

Answer 14

I think that it cant be linear. its just a guess

Answer 15

Not good if it is a guess! lol But you're right.
Let me try to explain:
The change per metre (sorry, I'm used to this spelling) is what?

Answer 16

the change per meter is the intensity of light right?

Answer 17

Yes, what is the change in intensity per metre?

Answer 18

3.4%

Answer 19

Excellent!
If we started with 1500 lumens, how much light is dissipated (lost) in the first metre?

Answer 20

do I have to subtract 3.4% to 1500?

Answer 21

Yes, take off 3.4% of 1500=51 lumens, right?

Answer 22

yes

Answer 23

We that leaves us with 1500-51=1449 lumens at the beginning of the second metre.
ok so far?

Answer 24

yup

Answer 25

How many lumens will be lost in the second metre?

Answer 26

is it 1448

Answer 27

Not exactly, you just subtracted 1 lumen from 1449, but we need to subtract 3.4% of 1449, so what is lost in the second metre is
1449*3.4%=49.3 lumens.

Answer 28

oh ok

Answer 29

Now here's the key question:
Can a linear function have a different "rate of change" at each metre?

Answer 30

I don't think so

Answer 31

There you go:
we have just demonstrated that the rate of change is not constant, so the conclusion is:________________________

Answer 32

this situation cannot be linear because in the first meter 1448 lumens are lost and in the second meter 49.3 lumens are lost therefore linear functions cannot have a different rate of change at each meter

Answer 33

Excellent! So we finished part A, right?

Answer 34

Except the first metre only lost 51 lumens....:(

Answer 35

ok ill change that and yes that was part A can we go to part b?

Answer 36

If we lose 3.4% each metre, how much (in percent) do we have left at the beginning of the next metre?

Answer 37

is it 47.6

Answer 38

I think you mean (100-3.4)=96.6%! :)

Answer 39

and 96.6% can be written as 0.966, do you agree?

Answer 40

oh ok haha :3

Answer 41

So light will decrease from 1500 lumens, decrease to 0.966 of the previous value for every metre it goes through.
Can you tell me what kind of function can model kind of behaviour?

Answer 42

I have no idea on this one o.O

Answer 43

Does this ring a bell?