Question

1. Fiber-optic cables are used widely by broadcast and cable companies. When light passes through a fiber-optic cable, its intensity decreases with the increase in the length of the cable. If 1000 lumens of light enters the cable, the intensity of light decreases by 1.2% per meter of the cable.

Part A: Can this situation be represented by an exponential 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 8 lumens per unit length of the cable. Can this situation be represented by an exponential function? Justify your answer and write the appropriate function to represent this situation if 1000 lumens of light enter the cable.

Answer 1

A: Yes. A function with a gradient that's dependent only on the value of the function is an exponential function.

B:
`f(x) = 1000*0.988^(x)`

C: No. If the rate of decrease is constant, it's a linear function.


`f(x) = -8x + 1000`