5. Holly wants to invest $1000. The table below shows the value of her investment under two
different options for two different years:
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: Holly 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 by
showing the investment value after 20 years for each option. (4 points)
Part A:
Is Option 1 Linear or Exponential?
Is Option 2 Linear or Exponential?
Explain your answer:
Part B:
Write a function for Option 1: f(n) =
Write a function for Option 2: f(n) =
Unit 4 Part 2
Template
Part C:
Plug and chug! Plug in 20 years to Option 1:
Plug and chug! Plug in 20 years to Option 2:
Which option has the higher value after 20 years?
Ms.Sue can you help me please
I'm sorry, but I don't know this math either.
Part A: To determine whether Option 1 and Option 2 can be described by linear or exponential functions, we need to assess the relationship between the value of the investment and the number of years.
If the value of the investment increases or decreases at a constant rate as the number of years increases, then it can be described by a linear function. On the other hand, if the value of the investment grows or declines at an increasing or decreasing rate as the number of years increases, then it can be described by an exponential function.
Part B: To write the functions for Option 1 and Option 2, we need to examine the table provided and find the pattern or equation that relates the value of the investment to the number of years.
Let's assume the value of the investment after n years for Option 1 is represented by f(n) and for Option 2 is represented by g(n).
Option 1:
Looking at the table, let's assume the initial value of the investment is $a and the value of the investment after one year is $b. We can calculate the rate of change as (b - a)/1.
For Option 1, if the rate of change is constant for each year, we can represent the linear function as:
f(n) = a + (b - a) * n
Option 2:
For Option 2, let's assume the initial value of the investment is $p and the value of the investment after one year is $q. We can calculate the ratio of change as q/p.
If the ratio of change is constant for each year, we can represent the exponential function as:
g(n) = p * (q/p)^n
Part C:
To determine which option would help Holly to increase her investment value by the greatest amount in 20 years, we need to calculate the value of each option after 20 years.
Plug and chug! Plug in 20 years to Option 1:
f(20) = a + (b - a) * 20
Plug and chug! Plug in 20 years to Option 2:
g(20) = p * (q/p)^20
By comparing the values obtained from both options, we can determine which option has the higher value after 20 years.