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.

Question

anonymous · Answer

Part A: Can this situation be represented by an exponential 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 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.

anonymous · Answer

A) the relation between intensity of light and length of the table is a linear relation. so it can not be represented as an exponential function

anonymous · Answer

B)

y = Ae^(kx)
A = 1200
1200*0.975=1200e^(k*1)
0.975 = e^k
k = ln 0.975 = -0.02532

y = 1200e^(-0.02532*x)