Question

PLEASE HELP! Medal & Fan Given.
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)

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)

Answer 1

Part C: Some scientists are trying to make a cable for which the intensity of light would decrease by 3 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 1200 lumens of light enter the cable. (4 points)

Answer 2

Part A: Yes, it can, because it gets multiplied by 2.5 for every meter it goes down the wire.
Part B: f(x) = 1200*2.5^x, because the initial value is 1200, and it increases 2.5 times for every meter.
Part C: No, it is decreasing at a constant rate. f(x) = 1200-3x, because it decreases by 3 for every meter.

Answer 3

Thank you :)