Question

Fiber-optic cables are used widely for wiring in aircraft and submarines. When light passes through a fiber-optic cable, its intensity decreases with the increase in the length of the cable. If 1200 lumens of light enters the cable, the intensity of light decreases by 2.5% per meter of the cable.

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

Answer 1

@jim_thompson5910

Answer 2

Any ideas?

Answer 3

A) Yes, the intensity of light decreases by the same factor every meter. So if we start with initial light intensity of 1200, it becomes 1200*.975 at x = 1 meter,
1200*.975*.975 at x = 2 meters, 1200*.0975^3 at x = 3, etc.. and so this is an exponential decay function.

B) It decreases BY 2.5% every meter.
So it decreases TO (100-2.5) = 97.5% or a factor of 0.975 every meter.

f(x) = 1200*(0.975)^x
f(x)=1200×0.975x

Answer 4

im not sure how to do it @jim_thompson5910

Answer 5

hope this helped!

Answer 6

thank you @mjoxprm360

Answer 7

need any additional details?

Answer 8

Anytime

Answer 9

@mjoxprm360 the last two equations aren't equivalent, how did an exponential become a times?

Answer 10

I'm sorry part 2 should not have been included i just put that there in case you needed it.

Answer 11

but you are right, the function is exponential.

Answer 12

Yes

Answer 13

For further discussion:

Light or electromagnetic spectrum is a bit complicated. For simplicity, as monochromatic light passes from vacuum to a medium its velocity decreases, and the same goes from one medium to another medium; and this decrease causes the intensity of the light to change as well. As the velocity decreases, the frequency remains the same. If the frequency remains the same, then two variables of the equation c = f λ must affect each other - the velocity, c, and the wavelength λ. And as observed, different wavelengths represent varying colors. With that in mind, think of white light that is made up various wavelengths in which we measure in lumens.

Answer 14

Thanks!