well, do part B and you will have the answer to part A
100 - 1.9 = 98.1 percent
so every time we go a meter, we multiply by .981
after x meters
f(x) = 1700 * .981^x (Part B answer)
which is exponential, not linear. (part A answer) It does not lose a constant "amount" per meter but a constant "fraction".
in part C, a constant "amount" is lost per meter so this is indeed linear (if impossible)
I = 1700 - 2 x
f(x) =
Fiber-optic cables are used widely to increase the speed and accuracy of data transmission. When light passes through a fiber-optic cable, its intensity decreases with the increase in the length of the cable. If 1700 lumens of light enters the cable, the intensity of light decreases by 1.9% per meter of the cable.
Part A: Can this situation be represented by a linear function? Justify your answer. (2 points)
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. (4 points)
Part C: Some scientists are trying to make a cable for which the intensity of light would decrease by 2 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 1700 lumens of light enter the cable. (4 points)
1 answer