Question

looooonnnnngggggg question...

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

hm it depends is the decrease in intensity cumulative? That is, does it reduce by 1.9% of the initial amount or does it change as you lose intensity?

If it's not cumulative you can write it as a linear expression: f(x)=1700−(0.019x)

If it's cumulative it would be exponential: \(\sf f(x)=1700e^{-0.019x}\)
^This more or less fits it, though it's not dead on