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.

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 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.

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.

ashy98 · Answer

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.

ashy98 · Answer

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.

ashy98 · Answer

@Riddellikins  does that look right to you?

anonymous · Answer

Nice work so far. Everything else is correct but there is a slight technical error in your exponential function.

If the light intensity decreases by 2.5%, then it will have 97.5% of the original intensity. You must then convert this percentage into a decimal and this forms the base of your exponential function. Do you think you can amend your function now?

anonymous · Answer

With your function currently, the light intensity value increases with the length of cable, but logic says that it must at least decrease.

ashy98 · Answer

for what part?

ashy98 · Answer

The intensity decreases by the same amount of 3 lumens every meter.  The difference in the y value is the same for every meter along x.  The slope is constant and therefore this is a linear function and not an exponential function.

f(x) = 1200 - 3x  or
f(x) = -3x + 1200  is the function.

ashy98 · Answer

@Riddellikins

anonymous · Answer

I am talking about Part B

anonymous · Answer

The exponential function "f(x) = 1200*2.5^x"

ashy98 · Answer

ohh okay thank you!