Answer and explanation:
Given: Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331
To find:
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?
Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years.
Part C: Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1?
Solution:
Part A: Linear and exponential functions can be used to describe the value of the investment after a fixed number of years using option 1 and option 2, respectively.
Part B: (n=n+100) and (n=n+100x) are the functions for each option to describe the value of the investment f(n), in dollars, after n years.
Part C: Yes, there will be a significant difference of 1900 in the value of Belinda's investment after 20 years if she uses option 2 over option 1.
Part A:
In the case of option 1, the linear function can be used to describe the value of the investment after a fixed number of years. This is because, in option one, the amount increases by a fixed amount every year.
In the case of option 2, the exponential function can be used to describe the value of the investment after a fixed number of years. This is because, in option 2, the amount increase is higher than last year.
Part B:
For option 1, the function is
For option 2, the function is
Here, x is the increase in amount every consecutive year.
Part C:
After 20 years, the amount from option 1 would be 3000 and the amount from option 2 would be 4900. Thus, there is a difference between 1900.
Therefore,
Part A: Linear and exponential functions can be used to describe the value of the investment after a fixed number of years using option 1 and option 2, respectively.
Part B: (n=n+100) and (n=n+100x) are the functions for each option to describe the value of the investment f(n), in dollars, after n years.
Part C: Yes, there will be a significant difference of 1900 in the value of Belinda's investment after 20 years if she uses option 2 over option 1.
Hope this helps
