Question

I've been stuck for some time on this, if someone would be willing to help me with it. :s

Answer 1

Fiber-optic cables are used widely to increase the speed and accuracy of data transmission. When light passes through a fiber-optic cable, its intensity decreases with the increase in the length of the cable. If 1700 lumens of light enters the cable, the intensity of light decreases by 1.9% per meter of the 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 2 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 1700 lumens of light enter the cable. (4 points)

Answer 2

since there is a percentage, I would use an exponential model

Answer 3

I'm afraid I'm not the most hyped up on Algebra due to an immense amount of history. I'm not sure how to start this. I do think its a linear function though.

Answer 4

I would say it is not linear, and rather a exponential, because a non-constant linear function function would approach
\[-\infty/\infty \] for large enough distance, which doesn't make any sense, because the light should become weaker, not infinitely strong at a distance. Also I don't think negative intensity exists.

Answer 5

try this model

y = A ( 1 + r) ^x
or
y = A ( 1 - r ) ^x

Answer 6

y = 1700 ( 1- 1.9/100 ) ^x works :)

Answer 7

You could try solution of the form:
\[f(x)=Ae^{-Bx}\]
Where A and B are constants you need to find based off of the conditions given

Answer 8

or
y = 1700 ( 1 - .019 ) ^x

Answer 9

@uhhhhhh can you explain how you got -infinity / infinity

Answer 10

pikatchu

Answer 11

If it was line with any non zero slope, it would approach positive or negative infinity as distance increased. Therefore it can't be linear.