Question

help?

Answer 1

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. (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 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. (4 points)

Answer 2

A i think is no not sure tho...

Answer 3

Exponential functions are represented by and occurrence of an event that is the same and occurs over and over. So can the above be shown as an exponential function?

Answer 4

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Answer 5

i dont think so cause its continually being mulitpied by 0.025 or 0.25 idk and not by itself i think.... im not tht bright

Answer 6

The intensity of light is continually multiplied by (1 - 0.025) = 0.975.
Yes, it can be represented as an exponential function.

Answer 7

IMosiac is correct

Answer 8

oh lol told ya im not tht bright xD

Answer 9

so for part b?

Answer 10

You start with light intensity of 1200 lumens. 1 meter later, the light intensity will be 1200 * 0.975. Two meters later, the light intensity will be 1200 * 0.975 * 0.975. So x meters later, the intensity will be ?

Answer 11

The decrease in lumens of light is a function of what?

Answer 12

1\[1200 \times 0.975^3\]

Answer 13

\(\Large f(x) = 1200 \times 0.975^x\)

Answer 14

whoops lol

Answer 15

and for part C?

Answer 16

As you can see for part B, it is a geometric progression because the common ratio is 0.975. But for part C, the decrease is always the same, a constant of 3 lumens. The difference between successive terms is a constant. This will be an arithmetic progression. Therefore, it cannot be represented as an exponential function.

Answer 17

say whaaa? lol

Answer 18

For part C) You start with 1200 lumens. 1 meter later the light intensity decreases by 3 and so it becomes 1200-3=1197. Two meters later it becomes 1200-3-3=1194.
So x meters later, the light intensity will be 1200 - 3*x.
So f(x) = 1200 - 3x.

Answer 19

oh ok so it can be represented by an exponential fnction and the eqation is f(x) = 1200 - 3x?

Answer 20

It CANNOT be represented as an exponential function. The f(x) is not \(f(x) = 1200 - 3^x\) but \(f(x) = 1200 - 3x\). There is no exponent. It is a linear equation. If you plot the graph it will be a straight line.

Answer 21

oh ok Thank You so much mosaic and sorry about late responses xD slow internet

Answer 22

np. yw.