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.

Answer 1

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.

Answer 2

@Thehulk49

Answer 3

Hold on

Answer 4

The answer to the question would be
A ... 2.5 % of 2.5% of 2.5% ... loss each meter ... yes repeated multiplication can be exponential.
Lo = original luminescence?? (or luminosity??) ... x = distance in meters
B. L(x) = Lo (1 - 0.025)^x
L(x) = 1200(0.975)^x

C. no, this would be a linear function. decrease 3 lumens , then 3 lumens ... this would be a sum loss of 3 + 3 + .... or -3x ... negative because of loss.
L(x) = 1200 - 3x

Answer 5

Now I got to do part A

Answer 6

The answer to part A would be this situation cannot be represented by an exponential function.

Answer 7

I don't understand

Answer 8

Where did I lose you at

Answer 9

This pqrt: The answer to part A would be this situation cannot be represented by an exponential function.

Answer 10

@Thehulk49

Answer 11

This is the question "Can this situation be represented by an exponential function? Justify your answer" and the answer is no

Answer 12

ohhhh ok @Thehulk49

Answer 13

Yea

Answer 14

Belinda wants to invest $1000. The table below shows the value of her investment under two different options for two different years:



Number of years 1 2 3
Option 1 (amount in dollars) 1100 1210 1331
Option 2 (amount in dollars) 1100 1200 1300


Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)

Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)

Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option.

Answer 15

@Thehulk49