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 1,500 lumens of light enter the cable, the intensity of light decreases by 3.4% per meter of 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.

Part C: Some scientists are trying to make a cable for which the intensity of light would decrease by 5 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 1500 lumens of light enter the cable.

Answer 1

Are these right?
A. No - the decrease in is not a constant

The intensity I of x meters of cable is I = 1500 * 0.964^x

C yes ?

Answer 2

A correct
B correct, except that I think you mean 0.966^x
C yes: C = 1500-5x