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)

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)

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)