Question

HELP PLEASE!!!!!!!!!!!!

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)

Answer 1

100-1.9 because each meter you lose a 1.9 percent of the original light length. but you keep 98.1 percent of the light

Answer 2

y=1700−2x
which is linear for part a

Answer 3

because i feel like part c the answer is its a linear equation of
y=1700−98x
so i think that part a and b are no the equation would be
y=1700ex∗98.1

Answer 4

Omg Thank you so much I was extremely confused!

Answer 5

Np

Answer 6

Could you also help me something else Algebra is not my thing?

Answer 7

yea

Answer 8

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) 1300 1600 1900
Option 2 (amount in dollars) 1120 1254.40 1404.93


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. Which option should Belinda choose? Explain your answer, and show the investment value after 20 years for each option. (4 points)

Answer 9

Part A - Option 1 is linear and it is simple interest

Answer 10

Ok and wouldnt the equation be 300x+1000??

Answer 11

yes an okay on to part B

Answer 12

Okk

Answer 13

Option 1
Total = 1,000 + (1 + n*.3)
n = number of years
the interest rate is a whopping 30% per year (but it is simple interest).

Here's some calculations from year zero to year 21

0 1,000.00
1 1,300.00
2 1,600.00
3 1,900.00
4 2,200.00
5 2,500.00
6 2,800.00
7 3,100.00
8 3,400.00
9 3,700.00
10 4,000.00
11 4,300.00
12 4,600.00
13 4,900.00
14 5,200.00
15 5,500.00
16 5,800.00
17 6,100.00
18 6,400.00
19 6,700.00
20 7,000.00
21 7,300.00

Answer 14

Total = $1,000 * (1 + rate)^n
The rate here is 12% but it is compound interest and again 'n' is years

Here are some calculations from year zero to year 21.
0 1,000.00
1 1,120.00
2 1,254.40
3 1,404.93
4 1,573.52
5 1,762.34
6 1,973.82
7 2,210.68
8 2,475.96
9 2,773.08
10 3,105.85
11 3,478.55
12 3,895.98
13 4,363.49
14 4,887.11
15 5,473.57
16 6,130.39
17 6,866.04
18 7,689.97
19 8,612.76
20 9,646.29
21 10,803.85

Note that at year 16, option 2 produces more money than option 1.
Although option 2 has a much smaller interest rate (12%) (compared to 30%), it is compound interest.

Answer 15

Ok so even though Option one has a higher interest rate Option 2 will eventually have a greater amount of money Right?

Answer 16

option 1 rate is 30% but use .3
option 2 is 12% but use .12

Answer 17

Okay I understand so for part C Belinda would choose Option 2 because it has an amount of 9,646.29 dollars after 20 years. While Option 1 only has a profit of 7,000.00 after 20 years.

Answer 18

Yes

Answer 19

Okay thank you so much for your help!

Answer 20

Welcome