Question

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 1690 2197
Option 2 (amount in dollars) 1300 1600 1900


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

Answer 1

@happylittlepill123 @LizzyMcWire @samantha1995 @Prototype93

Answer 2

Ill medal if you answer! :)

Answer 3

For part A, do you know how to tell if it's a linear or exponential function?

Answer 4

All the information is here. So I guess not.

Answer 5

Linear implies that the rate it's increasing by is flat, while exponential means the rate is changing over time, whether it be increasing or decreasing. Knowing that, what would you label each of the options as?

Answer 6

:E I dont really know.. This thing is timed can you just answer in these parts?

Answer 7

Option 1 is exponential because the rate that it's increasing by isn't the same each year, while option 2 is linear since it increases by 300 each year

Answer 8

Ok

Answer 9

Option 2?

Answer 10

I answered that too

Answer 11

How would you explain it though? just like how you did above?

Answer 12

The rate is flat

Answer 13

Option 2 because the rate is flat

Answer 14

Ok now part b?

Answer 15

Part b is stumping me tbh, although for option 2 its just 1300 + 300n

Answer 16

Option 1 will look something like 1300 + 300n * 1.3^n, but that's not perfect I know

Answer 17

Ok Part C?

Answer 18

Part c just says Belinda, Idk what I have to do

Answer 19

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. (4 points)

Answer 20

There will be a big difference, but you need to know the equation for option 1 to find the exact difference. Unfortunately I still can't help with that =/

Answer 21

Yikes. Ok can you help me with another problem?

Answer 22

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 23

@LizzyMcWire @Lost??? @OOOPS