Fiber-optic cables are used widely for internet wiring, data transmission, and surgeries. When light passes through a fiber-optic cable, its intensity decreases with the increase in the length of the cable. If 1500 lumens of light enters the cable, the intensity of light decreases by 3.4% per meter of the cable.

Part A: Can this situation be represented by a linear function? Justify your answer.

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.

Question

Fiber-optic cables are used widely for internet wiring, data transmission, and surgeries. When light passes through a fiber-optic cable, its intensity decreases with the increase in the length of the cable. If 1500 lumens of light enters the cable, the intensity of light decreases by 3.4% per meter of the cable.

Part A: Can this situation be represented by a linear function? Justify your answer. 

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.

anonymous · Answer

dI/dx = -0.034 I  will give an exponential dependence

I(x) = I(0) exp(-0.034x)