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.

Answer 1

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 2

Can someone help me with these

Answer 3

@zepdrix @dan815

Answer 4

@tester97 @mathmale

Answer 5

@jcpd910

Answer 6

Okay, here we go.
y = mx + b
y = -51 + 1500

The slope is -51 because our lumens are decreasing from 1500, and because we started with 1500, our y intercept is 1500.

And:
f(m) = 1500 - 1500(0.034)m

Answer 7

For part C, we are creating another linear equation.
If our slope is -5, where it decreases 5 lumens per unit length, then our equation is:
y = -5 + 1500

Answer 8

Remember, it's written as
y = -51x + 1500
and
y = -5x + 1500

Answer 9

because we need our x coordinate to have a definition.

Answer 10

ok gotchu